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catsarebad

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## Homework Statement

A:B→B a linear operator

Show r is multiple root for minimal polynomial u(x) iff

>$$\{0\}\subset \ker(A - rI) \subset \ker(A - rI)^2$$

note: it is proper subset

## Homework Equations

## The Attempt at a Solution

## Homework Statement

My thought:

I know ker(A−rI) is basically {{0} and {eigenvectors associated with r}}.

what is ker((A−rI)^2) with respect to above and/or r? How is eigenvector of (A−rI)^2 related to that of (L−rI)?

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