"Suppose that T : V -> V is a linear transformation of vector spaces over(adsbygoogle = window.adsbygoogle || []).push({});

R whose minimal polynomial has no multiple roots. Show that V can be

expressed as a direct sum

V = V1 + V2 + · · · + Vt

of T-stable subspaces of dimensions at most 2. Show that, relative to a suitable basis, T can be represented by an n × n matrix with at most 2n non-zero entries, where n := dim(V)."

Our professor is a little behind in lectures, but our assignments are still rolling full speed ahead. I'm not sure where to start. Can someone give me a hint?

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# Homework Help: Direct Sums

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