Consider (R) with respect to the Frobenius inner product defined by <A,B>=tr( A).Find the formula for the orthogonal projection P: (R) (R) on W, where

W=span{ .

My attempt:

The first step is to calculate an orthonormal basis for W and using the Gram Schmidt process I found that {X,Y}={ is already an orthonormal basis. Is there a way to check this without using the Gram Schmidt process?

In R B* is just the transpose of matrix B so:

Next I said:

P( =< , > + < , >

and I end up with

P( =

Is the method correct? If not where am I going wrong? Is the answer correct? If not where did I go wrong?

Any input would be appreciated.

Thanks in advance.