A square matrix A is called nilpotent if Ak = O for some k ¥ 1 (a)

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A square matrix A is called nilpotent if Ak = O for some k ‰¥ 1
(a) Show that

is nilpotent.
(b) Show that any strictly upper triangular matrix is nilpotent.
(c) Find a nilpotent matrix which is neither lower nor upper triangular.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 08:21 AM

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A square matrix A is called nilpotent if Ak = O for some k ¥ 1 (a)

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a By direct computation and so A 3 O b Let A have size n n By ...View the full answer

Applied Linear Algebra

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