Does there exists a matrix A ∈ Mn(F) such that $I, A, A^2 , ..., A^n$ are linearly independent in the vector space Mn(F)?
I'm not sure if this is even true or not. How would i go about solving this?
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Does $A2$ mean $A^2$? Does $An$ mean $A^n$? – José Carlos Santos May 19 '21 at 18:01
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Yes my bad. Edited now – LTM May 19 '21 at 18:04
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See also this post – Ben Grossmann May 19 '21 at 19:11