(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let W be a 1-dimensional subspace of V that is A-invariant. Show that every non zero vector in W is a eigenvector of A. [A element of M_{n}(F)]

3. The attempt at a solution

We know W is A-invariant therefore for all w in W A.w is in W. W is one dimensional which implies to me that A must therefore be a one by one matrix with an entry from F. Is this a correct assumption?

If so then A.w=λ.w where λ is an element of F which implies that all w in W are eigenvectors of A.

I'm new to this sort of linear algebra and therefore can't tell if I've made a blatant mistake?

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# Homework Help: Invariant spaces and eigenvector problem

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