Lecturenotes19-21January2011

Lecturenotes19-21January2011 - Back to matrix...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 4

Lecturenotes19-21January2011 - Back to matrix...

This preview shows document pages 1 - 2. Sign up to view the full document.

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