Find the derivative of f(X).
f(X) = transpose(a) * X * b
X is nxn
a and b are n x 1
ai is the i'th element of a
Xnm is the element in row n and column m
let transpose(a) = aT
let transpose(b) = bT
I tried using the product rule, which I assume is wrong.
I know the answer to be a*bT (but I have not the slightest clue how)
The Attempt at a Solution[/B]
I tried many things, to the point where punching a whole through my screen doesn't really seem like a bad idea anymore.
My last attempt was to use the product rule along with some matrix properties, here is what I did:
d(f)/dX = [d(aT*X)/dX]*b + (aT*X)*[d(b)/dX] = [d(aT*X)/dX]*b = (d/dX)[Σai*X1i Σai*X2i ⋅ ⋅ ⋅ Σai*Xni]*b
I have no idea what to do next. I have a feeling using the product rule doesn't apply to matrices.
PLEASE HELP ME!!!
Thanks for reading...