# 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.

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##### Solution Summary

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

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

T positive --> all ...

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