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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...
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This document was uploaded on 02/27/2014 for the course CS 215 at SIU Carbondale.
 Spring '14
 M.Nojoumian
 Computer Science

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