Let A be an invertible n n matrix. Show that the eigenvalues of A-1 are precisely

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Let A be an invertible n × n matrix.
Show that the eigenvalues of A-1 are precisely the numbers 1/λ, where λ is an eigenvalue of A.

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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 06:33 AM

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Let A be an invertible n n matrix. Show that the eigenvalues of A-1 are precisely

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If is an eigenvalue of A 1 then A 1 x x for some column x 0 0 because A 1 is invertible an...View the full answer

Linear Algebra With Applications

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