linear algebra review (optional) - jun jijun.hansung.ac.kr/ml/docs-slides-lecture3-kr.pdf ·...
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![Page 1: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/1.jpg)
Andrew Ng
Linear Algebra review (optional)
Matrices and vectors
Machine Learning
![Page 2: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/2.jpg)
Andrew Ng
행렬의차원: 행의수 x 열의수
Matrix: Rectangular array of numbers:
![Page 3: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/3.jpg)
Andrew Ng
Matrix Elements (entries of matrix)
“ , entry” in the row, column.
![Page 4: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/4.jpg)
Andrew Ng
Vector: An n x 1 matrix.
1-indexed vs 0-indexed:element
![Page 5: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/5.jpg)
Andrew Ng
Linear Algebra review (optional)
Addition and scalar multiplication
Machine Learning
![Page 6: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/6.jpg)
Andrew Ng
Matrix Addition
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Andrew Ng
Scalar Multiplication
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Andrew Ng
Combination of Operands
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Andrew Ng
Linear Algebra review (optional)
Matrix-vector multiplication
Machine Learning
![Page 10: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/10.jpg)
Andrew Ng
Example
![Page 11: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/11.jpg)
Andrew Ng
Details:
m x n matrix(m rows,
n columns)
n x 1 matrix(n-dimensional
vector)
m-dimensional vector
To get , multiply ’s row with elements of vector , and add them up.
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Andrew Ng
Example
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Andrew Ng
House sizes:
![Page 14: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/14.jpg)
Andrew Ng
Linear Algebra review (optional)
Matrix-matrix multiplication
Machine Learning
![Page 15: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/15.jpg)
Andrew Ng
Example
![Page 16: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/16.jpg)
Andrew Ng
Details:
m x n matrix(m rows,
n columns)
n x o matrix(n rows,
o columns)
m x omatrix
The column of the matrix is obtained by multiplyingwith the column of . (for = 1,2,…,o)
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Andrew Ng
Example
2 7
7
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Andrew Ng
House sizes:
Matrix Matrix
Have 3 competing hypotheses:
1.
2.
3.
![Page 19: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/19.jpg)
Andrew Ng
Linear Algebra review (optional)
Matrix multiplication properties
Machine Learning
![Page 20: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/20.jpg)
Andrew Ng
Let and be matrices. Then in general,
(not commutative.)
E.g.
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Andrew Ng
Let
Let
Compute
Compute
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Andrew Ng
Identity Matrix
For any matrix ,
Denoted (or ).Examples of identity matrices:
2 x 23 x 3
4 x 4
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Andrew Ng
Linear Algebra review (optional)
Inverse and transpose
Machine Learning
![Page 24: Linear Algebra review (optional) - Jun Jijun.hansung.ac.kr/ML/docs-slides-Lecture3-kr.pdf · 2016-09-01 · Linear Algebra review (optional) Matrix multiplication properties Machine](https://reader033.vdocuments.mx/reader033/viewer/2022042415/5f2fdb9c1db29717955a7a41/html5/thumbnails/24.jpg)
Andrew Ng
모든수가역수를가지지는않는다.
Matrix inverse:If A is an m x m matrix, and if it has an inverse,
역이없는행렬을 “singular” 또는 “degenerate” 라한다.
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Andrew Ng
Matrix Transpose
Example:
Let be an m x n matrix, and let Then is an n x m matrix, and