shivangi matrices
TRANSCRIPT
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SUBMITTED BY,
SHIVANGI RATHORE
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DEFINITIONSMatrix
Matrix is defined as a rectangular array of
numbers
A table of number or set of number
The numbers inside the matrix is calledelements or entries.
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TYPES OF MATRICES
1 . RECTANGULAR MATRIX
2. SQUARE MATRIX
3. ROW AND COLUMN MATRIX
4. DIAGONAL MATRIX
5. SCALAR MATRIX
6. UNIT MATRIX
7. ZERO MATRIX
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SIZE AND DIMENSION OF MATRIX
The size, or dimension, of the matrix is n x m, where, n is the number of rows of the matrix,
m is the number of column of the matrix.
For example, the following matrices are of dimensions 1x4,3x1, 2x3, and 4x2 respectively
A special kind of matrix is a square matrix ,
i.e. a matrix with the same number of rows and columns. If a square matrix has n rows and n columns, we say that the
matrix has order n.
The matrix is a square matrix of order 3.
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OPERATIONS IN MATRICES
Addition: Z = A + B; zij = aij + bij
Substraction: Z = A - B; zij = aij - bij
Multiplication: Z = A*B, if # columns in A = # rows inB; zij = ai1* b1j + ai2* b2j + ai3* b3j + ... aim* bnj
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Application of MatricesGraph theory
The adjacency matrix of a finite graph is a basic notion of graph
theory.
Linear combinations of quantum states in Physics
The first model of quantum mechanics by Heisenberg in 1925
represented the theory's operators by infinite-dimensionalmatrices acting on quantum states. This is also referred to as
matrix mechanics .
Computer graphics
44 transformation rotation matrices are commonly used incomputer graphics.
Solving linear equations
Using Row reduction
Cramer's Rule ( Determinants)
Using the inverse matrix
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CRYPTOGRAPHY
Cryptography, is concerned with keeping communications private.
Cryptography mainly consists of Encryption and Decryption
Encryption is the transformation of data into some unreadable form.
Its purpose is to ensure privacy by keeping the information hidden from
anyone for whom it is not intended, even those who can see the encrypteddata.
Decryption is the reverse of encryption
It is the transformation of encrypted data back into some intelligible form.
Encryption and Decryption require the use of some secret information, usually
referred to as a key.
Depending on the encryption mechanism used, the same key might be used
for both encryption and decryption, while for other mechanisms, the keys used
for encryption and decryption might be different.
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[MESSAGE] x [ENCRYPTION MATRIX] = [CODE]
[DECRYPTION MATRIX] x [CODE] = [MESSAGE]
Order of Encryption/Decryption Matrix must match
the length of message chunks and code (message chunk
length = number of entries in any column or row.
The encryption matrix MUST be invertible, otherwise
you cannot decode the message you encoded
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TIME MANAGEMENT MATRIX: THE 4
QUADRANTS
Our daily activities can be broken down into 4 quadrants,by urgency and importance:
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OTHER APPLICATIONS OF
MATRICES ECONOMICS: Checking out the production level of firm keeping
various factors in concern. VIDEO SCREEN
DIGITAL PHOTOGRAPHY
MARKETING :marketing strategy involves connectivity. Seeingand understanding the complex relationships between lawyersand clients, between value and client loyalty, between supply
and demand, between recurrent and non-recurrent client needsfor services, between referral sources and end-consumers
BUSINESS ORGANIZATIONS: TOWS AND SWOT.
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THANK YOU