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Math Help - Dimension problem

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    Dimension problem

    Let A be an nxn matrix. Prove that dim(span( \{ I_n ,A,A^2... \} )) \leq n
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    Quote Originally Posted by tttcomrader View Post
    Let A be an nxn matrix. Prove that \dim(\text{span}( \{ I_n ,A,A^2... \} )) \leq n
    This is easy if you know the Cayley–Hamilton theorem, which tells you that A^n is a linear combination of lower powers of A.
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