Let A be an nxn matrix. Prove that $\displaystyle dim(span( \{ I_n ,A,A^2... \} )) \leq n $
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Originally Posted by tttcomrader Let A be an nxn matrix. Prove that $\displaystyle \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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