# Thread: What area of mathematics would handle matrix differentiation?

1. ## What area of mathematics would handle matrix differentiation?

∂/∂x( x A T + (A xT + (xT A−1 x)(xT y))

Ts are the transposes and -1 are the inverses.

I understand partial differentiation wrt a variable.

I understand the matrix algebra of multiplying x by the transpose of a matrix.

I found some matrix identities but they don't help me understand why. Just need a place to start.

Thanks for any help.

2. Originally Posted by orangemoose
∂/∂x( x A T + (A xT + (xT A−1 x)(xT y))

Ts are the transposes and -1 are the inverses.

I understand partial differentiation wrt a variable.

I understand the matrix algebra of multiplying x by the transpose of a matrix.

I found some matrix identities by sam roweis but they don't help me understand why. Just need a place to start.

Thanks for any help.
Good book

3. ## That's a good book, but...

Right, but what I need is to find out what rules apply to that differentiation.

4. So you want $\partial (x A^T+ Ax^T+ (x^TA- Ix)(x^Ty))/\partial x$? (You have an extra left parenthesis.)

Is A a constant matrix or is it a function of x? In any case, as long as you are carefull not to commute a product, the usual derivative laws apply.

Assuming that A is a constant matrix, this is
$A^T+ A+ (A- I)(x^Ty)+ (x^TA- Ix)(y)$