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Exercise 7.2.12

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Denote $D_{k}$ to be the diagonal consisting of those $ij$ -entries such that $i - j = k$ . So $D_{0}$ is the original diagonal. If $A$ is upper triangular matrix whose entries in $D_{0}$ are all zero, we have the fact that the entries of $A^{p}$ in $D_{k}$ , $0 \leq k < p$ , are all zero. So $A$ must be nilpotent.

jephianlin

2011-06-27 00:00

Exercise 7.2.12

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