- #1
Bipolarity
- 776
- 2
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.
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
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