# Math Help - product of positive operators

1. ## product of positive operators

Let V be an inner product space with finite dimension. Suppose that T and U are two positive linear operators. I need an example to show that TU is not necessarily a positive operator.

2. ## Re: product of positive operators

How are you defining positive linear operator?

3. ## Re: product of positive operators

A linear operator T on an inner product space with finite dimension is positive if T is Hermitian and for every $\alpha \neq 0, (T\alpha|\alpha) >0$ (i.e. inner product of $\alpha$ and $T\alpha$ is positive).