Gradiant of XAY with respect to A How can I find the gradient of the following function with respect to A?
$$
F(A) = X^T \cdot A \cdot Y
$$
Where X and Y are mx1 vectors and A is mxm matrix

Writing
$F(A + \Delta A) = X^T A Y + X^T \Delta A Y$,
we see that
$F(A + \Delta A) - F(A) = X^T \Delta A Y$;
the error terms vanish exactly as they would for a plain old vanilla-flavored scalar function $f(x) =  ax$:
$f( x + \Delta x) - f(x) = a(x + \Delta x) - ax = a \Delta x$:
thus the derivative is a constant linear map; we have
$DF(\Delta A) = X^T (\Delta A) Y$.
The derivative  of any linear map is a constant and equal to the map itself.  For more info., see this Wikioedia page:  http://en.m.wikipedia.org/wiki/Matrix_calculus.
Hope this helps!
Cheers!
