# Trace on inner-product space.

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Suppose that V is an inner-product space. Prove that if T: V-->V is a

positive operator and trace(T)=0, then T=0.

https://brainmass.com/math/linear-algebra/trace-inner-product-space-75964

#### Solution Preview

Trace(T) = sum of all eigenvalues of T.

T positive --> all ...

#### Solution Summary

A trace on an inner-product space is investigated. Positive operators and trace functions are examined.

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