Let L V V be an invertible linear operator and let be an eigenvalue of L with associated eigenvector x (a) Show that 1 is an eigenvalue of L 1 with associated eigenvector x (b) State and prove the analogous statement for matrices ...

a Since Lx x and since L is invertible we have x L 1 x L 1 x Th ...

Let L: V - V be an invertible linear operator and let be an eigenvalue of

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Let L: V -→ V be an invertible linear operator and let λ be an eigenvalue of L with associated eigenvector x.
(a) Show that 1 / λ is an eigenvalue of L-1 with associated eigenvector x?
(b) State and prove the analogous statement for matrices?

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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 07:47 AM

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Let L: V - V be an invertible linear operator and let be an eigenvalue of

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a Since Lx x and since L is invertible we have x L 1 x L 1 x Th...View the full answer

Elementary Linear Algebra with Applications

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