Idempotent and nilpotent matrix proofs
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A matrix pxp matrix A is idempotent if A^2=A...
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Problem #3
If is idempotent, then . Suppose is an eigenvalue of and is the corresponding eigenvector, then we have . Then we have
This implies that or .
So each eigenvalue of an idempotent matrix is either or .
If is a nilpotent matrix, then for some positive integer . Suppose is an eigenvalue and is the corresponding eigenvector, then we have . Then we have
This implies ...
Solution Summary
This provides examples of proving several statements about an idempotent and a nilpotent matrix.
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