# Math Help - Diagonalizable tensor product

1. ## Diagonalizable tensor product

Hi everyone!

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

2. ## Re: Diagonalizable tensor product

Choose an eigenbasis for each $T,S$ and then form the standard tensor basis--I'm sure you'll find this is an eigenbasis for $T\otimes S$.