Matrix%20Algebra

# Matrix%20Algebra - Matrix Algebra Basic Introduction 1...

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Matrix Algebra : Basic Introduction 1. Matrix is a rectangular array of elements eg a 3x3 matrx A u a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 2. Distinguish column vector 1 2 3 from row vector 1 2 3 or 1, 2, 3 Often write row vector with a prime and column without 3. Transpose a matrix A signified A U means interchange all rows and colummns Transpose a vector b signified b U means make a row vector b a column vector. 4. Matrix addition: need to be the same size as add each of the elements to the corresponding ones in the other matrix. A ± B where a 11 a 12 a 21 a 22 ± b 11 b 12 b 21 b 22 u a 11 ± b 11 a 12 ± b 12 a 21 ± b 21 a 22 ± b 22 5. Multiply a matrix by a scalar: multiply all elements 6. Multiply vectors a U u a 1 a 2 a 3 and b u b 1 b 2 b 3 must be the same size ie of the same order then a U . b u a 1 a 2 a 3 b 1 b 2 b 3 u a 1 b 1 ± a 2 b 2 ± a 3 b 3 u a scalar 7. Matrix multiplication Consider A u a 11 a 12 a 21 a 22 B u b 11 b 12 b 21 b 22 A . B u a 11 b 11 ± a 12 b 21 a 11 b 12 ± a 12 b 22 a 21 b 11 ± a 22 b 21 a 21 b 12 ± a 22 b 22 Note that the first matrix needs to have the same number of columns as the second has rows.

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So can multiply 1 2 3 4 5 6 by 10 12 11 13 Note also that AB is not necessarily equal to BA so need to distinguish pre and post multiplication. If AB is defined then u AB U u U B u A u 8. Unit or identity matrix is a square matrix with ones down the diagonal and zeros elsewhere I 3 U 1 0 0 0 1 0 0 0 1 9. Determinant is an algebraic function of the elements of a matrix which is denoted |
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## This note was uploaded on 02/09/2011 for the course EEP 115 taught by Professor Waynem.getz during the Fall '10 term at Berkeley.

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Matrix%20Algebra - Matrix Algebra Basic Introduction 1...

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