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Eigenvalues for Linear Algebra Class.

Hi, I am having difficulties solving this problem. Please show all the steps involved.

1. An nxn matrix A is said to be nilpotent if A^k = O (the zero matrix) for some positive integer k. Show that all the eigen values of a nilpotent matrix are O.

Thanks.

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Proof:

Suppose A is a nilpotent matrix. By definition, there exists some positive integer k, such that A^k=0.
Now suppose c ...

Solution Summary

This solution is comprised of a detailed explanation to show that all the eigen values of a nilpotent matrix are O.

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