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Answer by Carlyle for Show that if all sub vectorspace are A-invariant, A...
Let $(v_i)_{i\in[n]}$ be a basis for $F^n$, you have already established that for each basis vector we must have$$Av_i =\lambda_{i}v_i $$Our goal is simply to show that for any $i,j\in[n]$, we have...
View ArticleShow that if all sub vectorspace are A-invariant, A must be scaled identity...
I'm trying to show the following:Let $A$ be an $n \times n$ matrix over a field $F$ such that every sub vectorspace of $F^n$ is invariant with respect to $A$, then $A$ must be of the form $\lambda I_n$...
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