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Matrices De
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Lecture 5: Homogeneous Equations and Properties of Matrices
dkatz.ku.eduIn order to de ne basic operations on matrices, we need to identify the elements in a matrix. Thus, if A is an m n matrix, whose entries are the real numbers a ij, then we call the element located on the ith row and jth entry of A, the (i;j)-entry of A. For example, given the matrices A =
SIMILAR MATRICES Similar Matrices - Mathematics
math.jhu.eduthat, by de nition, A= SBS 1 for some invertible S. Hence, A2 = (SBS 1)(SBS 1) = SB(S 1S)BS 1 = SBI nBS 1 = SB2S 1 and so A 2is similar to B . EXAMPLE: If Ais similar to Band one is invertible, then both are and A 1 is similar to B 1. Indeed, suppose Bis invertible, then A= SBS for invertible Sand so Ais also invertible as it is the product of ...