
Trace
I feel like I'm so close to solving this... I think I'm missing a step!?
I am to show that X = the pseudoinverse of A (I'll denote A+) will minimize AX  I_F and find the value of the minimum...
I started with AA+  I_F = (Tr((AA+  I)(AA+  I)*))^1/2 (by definition)
After some pseudoinverse properties and expansion, it boils down to
=(Tr(I  AA+))^1/2
Then I looked at the SVD of A, A = USV* and A+ = VE+U*
So
=(Tr(I  USV*VS+U*))^1/2 = (Tr(I  USS+U*))^1/2 because V is orthogonal... and here is where I'm stuck... please help!