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Unformatted text preview: Back to matrix multiplication: Recall for matrix addition we have zero matrix with A + 0 = 0 + A = A for any matrix A. We have a similar element called identity matrix I = 1 ... 1 ... . . . . . . . . . ... 1 such that AI = A . • Size of I must be adjusted for different matrices A. • If A is a m × n matrix, then I m A = AI n = A , I m = m × m identity matrix, I n = n × n identity matrix Note that I is like the number 1, (i.e. 1 · 2 = 2 , IA = A ). For numbers we have inverse of each number. Question: Do we have similar idea for matrices?= Do we have a multiplicative inverse for each matrix? Firstly what is the criteria for having an inverse? For numbers, if a is a number, we say b is its inverse if ab = ba = 1 . We denote by b = 1 a . So we will adapt the idea. Definition: If A is a square matrix and if a matrix B of the same size can be found such that AB = BA = I , then A is said to be invertible and B is called an inverse of A. If no such matrix B can be found, then A is said to be singular. Theorem 1.4.4 If B and C are both inverses of A, then B=C....
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This note was uploaded on 04/27/2011 for the course ENGR 130 taught by Professor Zhang during the Spring '11 term at University of Alberta.
- Spring '11