Take the following real matrices where , and is ...

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Take the following real matrices where. , and is positive-definite. Assume the columns of are orthonormal -dimensional vectors. Solve the expression.
Take the following real matrices where

,

and is positive-definite. Assume the columns of are orthonormal -dimensional vectors. Solve the expression while showing that the answer is independent of the particular vectors chosen to populate . It may help to consider that

is Hermitian and therefore qualifies for a diagonalization

and

It can also be proven (though I haven’t done so yet) that vectors in . is a function of .

is independent of your particular choice of