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Let $ K_n = \operatorname{span}\{b,Ab,\ldots,A^{n-1}b\} $. Also, show that $AK_n \subset K_n$ and $K_n = K_{n+1} = \cdots$.

These spaces are odd to me. Any ideas how to prove this?

Michael Hardy
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clocktower
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    It seems to me you must have missed a hypothesis, possibly that $n$ is the dimension of the space or the rank of $A$ or something like that. $\qquad$ – Michael Hardy Oct 19 '16 at 15:08

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