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.