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Math Help - Finding the Characteristic Polynomial of a Map

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    Finding the Characteristic Polynomial of a Map

    Let A: V \rightarrow V be a linear map satisfying the property A^2 = A. Assume that  dim V = n, rank A = k. Find the characteristic polynomial of A.

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

    Thanks!
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    Quote Originally Posted by h2osprey View Post
    Let A: V \rightarrow V be a linear map satisfying the property A^2 = A. Assume that  dim V = n, rank A = k. Find the characteristic polynomial of A.

    I don't really know where to start, is this an application of the Cayley-Hamilton Theorem or something?
    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 nk).
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    Of course, it's all clear now. Thanks!
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