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.

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- Aug 13th 2013, 07:26 AMxixiproduct 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.

- Aug 13th 2013, 12:31 PMHallsofIvyRe: product of positive operators
How are you defining

**positive**linear operator? - Aug 15th 2013, 08:42 PMHumanRe: 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 $\displaystyle \alpha \neq 0, (T\alpha|\alpha) >0$ (i.e. inner product of $\displaystyle \alpha$ and $\displaystyle T\alpha$ is positive).