atlab course - vgloop.com · -version of java software for the matlab product. the version numbers...
TRANSCRIPT
![Page 1: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/1.jpg)
Matlab Course
Lecture time: Sunday Off
Monday 8:00-10:00 12:00-2:00
Tuesday 14:00-16:00
Wednesday 10:00-12:00 14:00 - 16:00
Thursday 8:00 - 10:00
Location: Albiruni I\II Lab-B Building
Thaer Khatib, Palestine Polytechnic University © 1
![Page 2: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/2.jpg)
Note: The Matlab Software Would be on the Desktop in a file named Matlab _R2008A
For Homework's and any other information
Name| Section| HW#
Thaer Khatib, Palestine Polytechnic University © 2
![Page 3: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/3.jpg)
Matlab (matrix laboratory)
high-performance language for technical computing integrates
computation, visualization, and programming in an easy-to-use
environment where problems and solutions are expressed in
familiar mathematical notation.
Developed by MathWorks.
Thaer Khatib, Palestine Polytechnic University © 3
![Page 4: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/4.jpg)
Matlab (matrix laboratory)
Typical uses for Matlab
Math and computation
Algorithm development
Data acquisition
Modeling, simulation, and prototyping
Data analysis, exploration, and visualization
Scientific and engineering graphics
Application development, including graphical user interface building
Thaer Khatib, Palestine Polytechnic University © 4
![Page 5: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/5.jpg)
Installation Procedure
Thaer Khatib, Palestine Polytechnic University © 5
![Page 6: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/6.jpg)
6 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
![Page 7: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/7.jpg)
7 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
11111-11111-11111-02626
![Page 8: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/8.jpg)
8 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
![Page 9: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/9.jpg)
9 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
![Page 10: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/10.jpg)
10 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
![Page 11: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/11.jpg)
11 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
![Page 12: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/12.jpg)
12 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
license_standalone.dat
![Page 13: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/13.jpg)
13 Thaer Khatib, Palestine Polytechnic University ©
Installation Procedure
![Page 14: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/14.jpg)
14 Thaer Khatib, Palestine Polytechnic University ©
The Matlab environment
Command Window
Changing current directory
Prompt\Command line
Files and directories Inside the current directory
Command History
![Page 15: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/15.jpg)
15 Thaer Khatib, Palestine Polytechnic University ©
Matlab can be used as calculator
![Page 16: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/16.jpg)
16 Thaer Khatib, Palestine Polytechnic University ©
Our first command
Writing a command in the command line
![Page 17: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/17.jpg)
17 Thaer Khatib, Palestine Polytechnic University ©
Our first Scrip M-File
![Page 18: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/18.jpg)
18 Thaer Khatib, Palestine Polytechnic University ©
Making errors …
![Page 19: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/19.jpg)
19 Thaer Khatib, Palestine Polytechnic University ©
Example
Write a script:
University name
Your name and ID #
Specialization-department-college
Formal email
![Page 20: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/20.jpg)
20 Thaer Khatib, Palestine Polytechnic University ©
Identifiers
![Page 21: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/21.jpg)
21 Thaer Khatib, Palestine Polytechnic University ©
Identifiers
![Page 22: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/22.jpg)
22 Thaer Khatib, Palestine Polytechnic University ©
Reserved words (Keywords)
![Page 23: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/23.jpg)
23 Thaer Khatib, Palestine Polytechnic University ©
Reserved words (Keywords)
Special Variables pi, eps, ….
realmax, realmin, sin, cos, ….
sqrt(i), rem(i,j),…
![Page 24: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/24.jpg)
24 Thaer Khatib, Palestine Polytechnic University ©
Constants
![Page 25: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/25.jpg)
25 Thaer Khatib, Palestine Polytechnic University ©
Variables
![Page 26: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/26.jpg)
26 Thaer Khatib, Palestine Polytechnic University ©
Variables (cont.)
![Page 27: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/27.jpg)
27 Thaer Khatib, Palestine Polytechnic University ©
Variables (cont.)
![Page 28: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/28.jpg)
28 Thaer Khatib, Palestine Polytechnic University ©
Variables (cont.)
![Page 29: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/29.jpg)
29 Thaer Khatib, Palestine Polytechnic University ©
Operations on variables
![Page 30: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/30.jpg)
30 Thaer Khatib, Palestine Polytechnic University ©
List of variables
• Who
![Page 31: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/31.jpg)
31 Thaer Khatib, Palestine Polytechnic University ©
Array is the main data structure
used in Matlab
![Page 32: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/32.jpg)
32 Thaer Khatib, Palestine Polytechnic University ©
Examples of 1D and 2D arrays
![Page 33: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/33.jpg)
33 Thaer Khatib, Palestine Polytechnic University ©
Creating 1D Arrays
![Page 34: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/34.jpg)
34 Thaer Khatib, Palestine Polytechnic University ©
Creating 1D Arrays
![Page 35: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/35.jpg)
35 Thaer Khatib, Palestine Polytechnic University ©
Creating 1D Arrays
![Page 36: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/36.jpg)
36 Thaer Khatib, Palestine Polytechnic University ©
Creating 1D Arrays
![Page 37: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/37.jpg)
37 Thaer Khatib, Palestine Polytechnic University ©
Creating 1D Arrays
![Page 38: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/38.jpg)
38 Thaer Khatib, Palestine Polytechnic University ©
Creating 1D Arrays
![Page 39: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/39.jpg)
39 Thaer Khatib, Palestine Polytechnic University ©
Indexing 1D Arrays
![Page 40: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/40.jpg)
40 Thaer Khatib, Palestine Polytechnic University ©
Indexing 1D Arrays
![Page 41: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/41.jpg)
41 Thaer Khatib, Palestine Polytechnic University ©
Indexing 1D Arrays
![Page 42: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/42.jpg)
42 Thaer Khatib, Palestine Polytechnic University ©
Indexing 1D Arrays
![Page 43: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/43.jpg)
43 Thaer Khatib, Palestine Polytechnic University ©
Indexing 1D Arrays
![Page 44: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/44.jpg)
44 Thaer Khatib, Palestine Polytechnic University ©
Indexing 1D Arrays
![Page 45: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/45.jpg)
45 Thaer Khatib, Palestine Polytechnic University ©
Use indexing to edit 1D Arrays
![Page 46: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/46.jpg)
46 Thaer Khatib, Palestine Polytechnic University ©
Use indexing to edit 1D Arrays
![Page 47: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/47.jpg)
47 Thaer Khatib, Palestine Polytechnic University ©
1D Array Orientation
Note: difference btw (’) and (.’)
![Page 48: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/48.jpg)
48 Thaer Khatib, Palestine Polytechnic University ©
![Page 49: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/49.jpg)
49 Thaer Khatib, Palestine Polytechnic University ©
Reminder of previous lecture
• Introduction.
• Matlab installation.
• Matlab interface.
• Identifiers.
• Arrays.
• Indexing.
• Simple operations on arrays.
![Page 50: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/50.jpg)
50 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on 1D arrays
![Page 51: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/51.jpg)
51 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on 1D arrays
![Page 52: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/52.jpg)
52 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on 1D arrays
![Page 53: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/53.jpg)
53 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on 1D arrays
![Page 54: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/54.jpg)
54 Thaer Khatib, Palestine Polytechnic University ©
Sub-array searching
![Page 55: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/55.jpg)
55 Thaer Khatib, Palestine Polytechnic University ©
Sub-array searching
![Page 56: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/56.jpg)
56 Thaer Khatib, Palestine Polytechnic University ©
Sub-array searching
![Page 57: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/57.jpg)
57 Thaer Khatib, Palestine Polytechnic University ©
Arithmetic operations on 1D arrays
![Page 58: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/58.jpg)
58 Thaer Khatib, Palestine Polytechnic University ©
Arithmetic operations on 1D arrays
![Page 59: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/59.jpg)
59 Thaer Khatib, Palestine Polytechnic University ©
Arithmetic operations on 1D arrays
![Page 60: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/60.jpg)
60 Thaer Khatib, Palestine Polytechnic University ©
Arithmetic operations on 1D arrays
![Page 61: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/61.jpg)
61 Thaer Khatib, Palestine Polytechnic University ©
Matrices (2D Array)
![Page 62: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/62.jpg)
62 Thaer Khatib, Palestine Polytechnic University ©
Creating matrices
![Page 63: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/63.jpg)
63 Thaer Khatib, Palestine Polytechnic University ©
Creating matrices
![Page 64: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/64.jpg)
64 Thaer Khatib, Palestine Polytechnic University ©
Creating matrices
![Page 65: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/65.jpg)
65 Thaer Khatib, Palestine Polytechnic University ©
Creating matrices
![Page 66: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/66.jpg)
66 Thaer Khatib, Palestine Polytechnic University ©
Indexing matrices
![Page 67: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/67.jpg)
67 Thaer Khatib, Palestine Polytechnic University ©
Indexing matrices
![Page 68: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/68.jpg)
68 Thaer Khatib, Palestine Polytechnic University ©
Indexing matrices
![Page 69: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/69.jpg)
69 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 70: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/70.jpg)
70 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 71: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/71.jpg)
71 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 72: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/72.jpg)
72 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 73: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/73.jpg)
73 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 74: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/74.jpg)
74 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 75: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/75.jpg)
75 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 76: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/76.jpg)
76 Thaer Khatib, Palestine Polytechnic University ©
Using indexing to modify matrices
![Page 77: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/77.jpg)
77 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 78: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/78.jpg)
78 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 79: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/79.jpg)
79 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 80: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/80.jpg)
80 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 81: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/81.jpg)
81 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 82: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/82.jpg)
82 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 83: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/83.jpg)
83 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 84: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/84.jpg)
84 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 85: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/85.jpg)
85 Thaer Khatib, Palestine Polytechnic University ©
Simple operations on matrices
![Page 86: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/86.jpg)
86 Thaer Khatib, Palestine Polytechnic University ©
![Page 87: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/87.jpg)
87 Thaer Khatib, Palestine Polytechnic University ©
Reminder of previous lecture
• Simple operations on 1D arrays.
• Arithmetic operations on 1D arrays.
• Creating matrices.
• Indexing matrices.
• Simple operations on matrices.
• Arithmetic operations on matrices.
![Page 88: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/88.jpg)
88 Thaer Khatib, Palestine Polytechnic University ©
Plot command
![Page 89: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/89.jpg)
89 Thaer Khatib, Palestine Polytechnic University ©
Plot command
![Page 90: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/90.jpg)
90 Thaer Khatib, Palestine Polytechnic University ©
![Page 91: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/91.jpg)
91 Thaer Khatib, Palestine Polytechnic University ©
Subplot command
The subplot command allows you to subdivide the graphing window into a grid
of m rows and n columns. The function
splits the figure into an m X n matrix. The variable p identifies the portion of the window
where the next plot will be drawn. For example, if the command
![Page 92: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/92.jpg)
92 Thaer Khatib, Palestine Polytechnic University ©
Subplot command
Example:
x=0:0.1:2*pi;
subplot(2,2,1);
plot(x,sin(x));
subplot(2,2,2);
plot(x,cos(x));
subplot(2,2,3)
plot(x,exp(-x));
subplot(2,2,4);
plot(x,sqrt(x))
![Page 93: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/93.jpg)
93 Thaer Khatib, Palestine Polytechnic University ©
Complex numbers
The symbol "i" identifies the imaginary part and has to be typed
immediately after the numerical value of the imaginary part
![Page 94: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/94.jpg)
94 Thaer Khatib, Palestine Polytechnic University ©
Construct complex data from real and imaginary components
complex(x,y)
![Page 95: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/95.jpg)
95 Thaer Khatib, Palestine Polytechnic University ©
real(x), imag(x), abs(x)
![Page 96: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/96.jpg)
96 Thaer Khatib, Palestine Polytechnic University ©
Isreal(x), conj(x)
Determine whether input is real array
Complex conjugate
![Page 97: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/97.jpg)
97 Thaer Khatib, Palestine Polytechnic University ©
Cart2pol, pol2cart
![Page 98: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/98.jpg)
98 Thaer Khatib, Palestine Polytechnic University ©
Cart2pol, pol2cart
![Page 99: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/99.jpg)
99 Thaer Khatib, Palestine Polytechnic University ©
Cart2sph, sph2cart
Transform Cartesian coordinates to spherical
Transform spherical coordinates to Cartesian
cart2sph
sph2cart
![Page 100: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/100.jpg)
100 Thaer Khatib, Palestine Polytechnic University ©
Cart2sph, sph2cart
Transform Cartesian coordinates to spherical
Transform spherical coordinates to Cartesian
cart2sph
sph2cart
![Page 101: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/101.jpg)
101 Thaer Khatib, Palestine Polytechnic University ©
ver command
ver:
A header containing:
-The current MATLAB product family version number.
-license number.
-operating system.
-version of Java software for the MATLAB product.
The version numbers for MATLAB and all other installed
MathWorks products.
![Page 102: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/102.jpg)
102 Thaer Khatib, Palestine Polytechnic University ©
Calculus
The Symbolic Math Toolbox provides functions to do the basic
operations of calculus; differentiation, limits, integration,
summation, and Taylor series expansion.
Differentiation
diff(f)
differentiates f with respect to its symbolic variable (in this case x)
Let’s create a symbolic expression.
![Page 103: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/103.jpg)
103 Thaer Khatib, Palestine Polytechnic University ©
Calculus
![Page 104: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/104.jpg)
104 Thaer Khatib, Palestine Polytechnic University ©
Calculus
Limits
The fundamental idea in calculus is to make calculations on functions
as a Variable “gets close to” or approaches a certain value. Recall that
the definition of the derivative is given by a limit
provided this limit exists. The Symbolic Math Toolbox allows you to
compute the limits of functions in a direct manner
![Page 105: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/105.jpg)
105 Thaer Khatib, Palestine Polytechnic University ©
Calculus
Limits
The fundamental idea in calculus is to make calculations on functions
as a Variable “gets close to” or approaches a certain value. Recall that
the definition of the derivative is given by a limit
provided this limit exists. The Symbolic Math Toolbox allows you to
compute the limits of functions in a direct manner
![Page 106: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/106.jpg)
106 Thaer Khatib, Palestine Polytechnic University ©
Calculus
![Page 107: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/107.jpg)
107 Thaer Khatib, Palestine Polytechnic University ©
Calculus
![Page 108: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/108.jpg)
108 Thaer Khatib, Palestine Polytechnic University ©
Calculus
Integration
![Page 109: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/109.jpg)
109 Thaer Khatib, Palestine Polytechnic University ©
Calculus
![Page 110: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/110.jpg)
110 Thaer Khatib, Palestine Polytechnic University ©
Solving Equation
If S is a symbolic expression, solve(S) attempts to find values of
the symbolic variable in S for which S is zero. For example,
![Page 111: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/111.jpg)
111 Thaer Khatib, Palestine Polytechnic University ©
Solving Equation
This is a symbolic vector whose elements are the two solutions.
If you want to solve for a specific variable, you must specify that
variable as an additional argument. For example, if you want to
solve S for b, use the command
Note that these examples assume equations of the form f(x) = 0. If
you need to solve equations of the form f(x)=q(x) you must use
quoted strings. In particular, the command
![Page 112: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/112.jpg)
112 Thaer Khatib, Palestine Polytechnic University ©
Several Algebraic Equations
![Page 113: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/113.jpg)
113 Thaer Khatib, Palestine Polytechnic University ©
Linear algebra
![Page 114: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/114.jpg)
114 Thaer Khatib, Palestine Polytechnic University ©
Linear algebra
![Page 115: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/115.jpg)
115 Thaer Khatib, Palestine Polytechnic University ©
Linear algebra
![Page 116: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/116.jpg)
116 Thaer Khatib, Palestine Polytechnic University ©
Linear algebra
![Page 117: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/117.jpg)
117 Thaer Khatib, Palestine Polytechnic University ©
Polynomial Roots and Characteristic Polynomial
if p is a row vector containing the coefficients of a polynomial,
roots(p) returns a column vector whose elements are the roots
of the polynomial. If r is a column vector containing the roots
of a polynomial, poly(r) returns a row vector whose elements
are the coefficients of the polynomial.
![Page 118: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/118.jpg)
118 Thaer Khatib, Palestine Polytechnic University ©
Polynomial Roots and Characteristic Polynomial
![Page 119: atlab Course - vgloop.com · -version of Java software for the MATLAB product. The version numbers for MATLAB and all other installed MathWorks products. 102](https://reader031.vdocuments.mx/reader031/viewer/2022022021/5b9ff42e09d3f2385c8c99fa/html5/thumbnails/119.jpg)
119 Thaer Khatib, Palestine Polytechnic University ©
Polynomial Roots and Characteristic Polynomial