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Math Help - Any polynomial is the characteristic polynomial of some linear operator?

  1. #1
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    Any polynomial is the characteristic polynomial of some linear operator?

    Why is it that any polynomial of degree n with leading coefficient (-1)^n the characteristic polynomial of some linear operator?

    Also, how is this fact related to invariant subspaces?
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  2. #2
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    Quote Originally Posted by cubrikal View Post
    Why is it that any polynomial of degree n with leading coefficient (-1)^n the characteristic polynomial of some linear operator?

    Also, how is this fact related to invariant subspaces?

    Google "companion matrix"

    Tonio
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