Diagonalizable tensor product

• Dec 7th 2012, 04:19 AM
charles01
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.
• Dec 9th 2012, 09:57 PM
Drexel28
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 $T\otimes S$.