I have two questions:(adsbygoogle = window.adsbygoogle || []).push({});

1. Let V be a finite dimensional inner product space. Show that if U: V--->V is self-adjoint and T: V---->V is positive definite, then UT and TU are diagonalizable operators with only real eigenvalues.

2. Suppose T and U are normal operators on a finite dimensional complex inner product space V such that TU = UT

a) Show that UT* = T*U

b) show that there is an orthonormal basis for V consisting of vectors that are eigenvectors for both T and U

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# Homework Help: Normal, self-adjoint and positive definite operators

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