Matrix%20Algebra

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 |
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online