I am following Friedberg's text and having some trouble understanding some of the theorems regarding diagonalizability. The proofs seem to skip some steps, so I guess I need to work through them a bit more slowly.(adsbygoogle = window.adsbygoogle || []).push({});

Given a linear operator ## T:V → V ##, with eigenspaces ## \{ E_{ \lambda_{1}},E_{ \lambda_{2}},...E_{ \lambda_{k}} \} ##, is it true that ## E_{ \lambda_{1}} \bigoplus E_{ \lambda_{2}} \bigoplus E_{ \lambda_{2}} ... \bigoplus E_{ \lambda_{k}} = V ## ?

What if T is diagonalizable? This is just a thought which may perhaps help me to understand diagonalizability a bit better. I simply need to know whether this is right or not. Please no explanations, as I will prove it myself. Thanks!

BiP

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# Direct sum of the eigenspaces equals V?

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