(5) A square matrix A is called nilpotent if there exists a positive integer k such...

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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...
A square matrix A is called nilpotent if Ak = O for some k 1. (a) Prove that the only eigenvalue of a nilpotent matrix is 0. (The converse is also true; see Exercise 8.6.18.) (b) Find examples where...
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