Let A be a diagonalizable n n matrix with eigenvalues 1, 2, , n(including multiplicities) Show that (a) det A 12 n (b) trA 1 2 n ...

b Let P 1 AP D diag 1 2 n Since ...

Let A be a diagonalizable n n matrix with eigenvalues 1, 2, . . ., n(including

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Let A be a diagonalizable n × n matrix with eigenvalues λ1, λ2, . . ., λn(including multiplicities). Show that:
(a) det A = λ1λ2 . . . λn
(b) trA = λ1 + λ2 + . . . + λn

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Linear Algebra With Applications

ISBN: 9780070985100

7th Edition

Authors: W. Keith Nicholson

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Question Posted: Jun 21, 2016 06:39 AM

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Let A be a diagonalizable n n matrix with eigenvalues 1, 2, . . ., n(including

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