Square matrices do not change when their rows

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: f rows in the 2nd. Illustra$on of Matrix Mul$plica$on —༉  The Product of A = [aij] and B = [bij] Matrix Mul$plica$on is not Commuta$ve Example: Let Does AB = BA? Solution: AB ≠ BA Iden$ty Matrix and Powers of Matrices Definition: the identity matrix of order n is the m × n matrix In = [δij], where δij = 1 if i = j and δij = 0 if i ≠ j. AIn = ImA = A when A is an m × n matrix Powers of square matrices can be deWined. When A is an n × n matrix, we have: A0 = In also Ar = A A A … A r times Transposes of Matrices Definition: let A = [aij] be an m × n matrix. The transpose of A, denoted by At , is the n × m matrix obtained by interchanging the rows and columns of A. If At = [bij], then bij = aji for i =1, …, n and j = 1, …, m. Symmetric Matrices Definition: a square matrix A is called symmetric if A = At. Thus A = [aij] is symmetric if aij = aji for i and j with 1 ≤ i ≤ n and 1 ≤ j ≤ n. Square matrices do not change when their rows and columns are interchanged. Zero- One Matrices Definition: a matrix all of whose entries are either 0 or 1 is called a zero- one matrix. —༉  Algorithms operating on di...
View Full Document

This document was uploaded on 02/27/2014 for the course CS 215 at SIU Carbondale.

Ask a homework question - tutors are online