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**1. Homework Statement**

My statistical mechanics book says that if M is an real, symmetric n by n matrix, and U is the matrix of its eigenvectors as column vectors, then the transformation UMU^{-1} preserves the trace of M. Is that true? If so, is it obvious? If it is true but not obvious, how do you prove it?

**2. Homework Equations**

**3. The Attempt at a Solution**