# Linear Algebra - Self-adjoint...something something

Printable View

• Mar 9th 2008, 01:43 PM
Chloroform
Linear Algebra - Self-adjoint...something something
Let V be a finite dimensional inner product space. Show that the product of two self-adjoint linear maps S and T on V is self adjoint if and only if ST = TS

I have no idea what I am doing here.
• Mar 10th 2008, 06:54 AM
Opalg
Quote:

Originally Posted by Chloroform
Let V be a finite dimensional inner product space. Show that the product of two self-adjoint linear maps S and T on V is self adjoint if and only if ST = TS.

The adjoint of a product is the product of the two adjoints in the opposite order. In other words, $(AB)^* = B^*A^*$. That's all you need to know in order to do this problem.