Let A be an n*n matrix.(adsbygoogle = window.adsbygoogle || []).push({});

Consider the space [itex]span \{ I, A, A^2, A^3, ... \} .[/itex]

How would one show that the dimension of the space never exceeds n?

I feel like the answer lies somewhere near the Cayley-Hamilton theorem, but I can't quite grasp it.

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# Dimension of space composed of powers of a matrix

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