Let A be an m x n matrix and B an n x m matrix. Prove that Tr(AB)=Tr(BA). Recall that if C=[cij] is an n x n matrix, then the trace of C is Tr(|cij|)= c11+c22+...+ccnn.
Let A be an m x n matrix and B an n x m matrix. Prove that Tr(AB)=Tr(BA). Recall that if C=[cij] is an n x n matrix, then the trace of C is Tr(|cij|)= c11+c22+...+ccnn.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
Problem 63EQ
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Let A be an m x n matrix and B an n x m matrix. Prove that Tr(AB)=Tr(BA). Recall that if C=[cij] is an n x n matrix, then the trace of C is Tr(|cij|)= c11+c22+...+ccnn.
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