Hi everyone!

I have to prove that if T : V $\displaystyle \rightarrow$ V and S:V$\displaystyle \rightarrow$V are diagonalizable so T$\displaystyle \otimes$S is diagonalizable.

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- Dec 7th 2012, 03:19 AMcharles01Diagonalizable tensor product
Hi everyone!

I have to prove that if T : V $\displaystyle \rightarrow$ V and S:V$\displaystyle \rightarrow$V are diagonalizable so T$\displaystyle \otimes$S is diagonalizable. - Dec 9th 2012, 08:57 PMDrexel28Re: Diagonalizable tensor product
Choose an eigenbasis for each $\displaystyle T,S$ and then form the standard tensor basis--I'm sure you'll find this is an eigenbasis for $\displaystyle T\otimes S$.