If A = [ajj] is an n Ã n matrix, then the trace of A, Tr(A), is

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If A = [ajj] is an n Ã— n matrix, then the trace of A, Tr(A), is defined as the sum of all elements on the main diagonal of A,

Show each of the following:
(a) Tr(cA) = c Tr(A), where c is a real number
(b) Tr(A + B) = Tr(A) + Tr(B)
(c) Tr(AB) = Tr(BA)
(d) Tr(AT) = Tr(A)
(e) Tr(ATA) ‰¥ 0

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Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

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Question Posted: Jun 21, 2016 06:55 AM

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If A = [ajj] is an n Ã n matrix, then the trace of A, Tr(A), is

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Tr(A) Σαϊί

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a b c Let AB C C ij The...View the full answer

Elementary Linear Algebra with Applications

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