- #1

perplexabot

Gold Member

- 329

- 5

## Homework Statement

Find the derivative of f(X).

f(X) = transpose(a) * X * b

where:

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

## Homework Equations

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...