Let K be a field and A Mat n K. (a) If A is nilpotent (that

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Let K be a field and A ϵ Mat_nK.

(a) If A is nilpotent (that is, A^m = 0 for some m), then Tr A^r = 0 for all r ≥ 1.

(b) If char K = 0 and Tr A^r = 0 for all r ≥ 1, the~ A is nilpotent.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Aug 18, 2023 06:54 AM

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Let K be a field and A Mat n K. (a) If A is nilpotent (that

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a If A is nilpotent that is Am 0 for some m then Tr Ar 0 for all r 1 In this part youre asked to show that if a square matrix A is nilpotent meaning t...View the full answer

Algebra Graduate Texts In Mathematics 73

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