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
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, $\displaystyle (AB)^* = B^*A^*$. That's all you need to know in order to do this problem.