Finding the Characteristic Polynomial of a Map

Let be a linear map satisfying the property . Assume that Find the characteristic polynomial of

I don't really know where to start, is this an application of the Cayley-Hamilton Theorem or something?

Thanks!

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Originally Posted by h2osprey

Let be a linear map satisfying the property . Assume that Find the characteristic polynomial of

I don't really know where to start, is this an application of the Cayley-Hamilton Theorem or something?

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Hint: The image of A is the eigenspace for the eigenvalue 1 (and has dimension k). The null space of A is the eigenspace for the eigenvalue 0 (and has dimension n–k).

Of course, it's all clear now. Thanks!