I Differentiating Vectors: Solve the Problem Now!

[maistral]

Hi. I have this problem with differentiating vectors.

Primarily because I have no experience at all (or whatsoever) about differentiating vectors. I am at a total loss here. I even have no idea regarding the difficulty of this (thus the [ I ] prefix). Please help me.

How did the two equations below come out? Can someone show me formulas on how did these appear? What happened to the ^T?

I did search for resources over the net about formulas and I got even more confused.

The bolded variables are matrices... or vectors. I think.

 

[Mark44]

Hi. I have this problem with differentiating vectors.

Primarily because I have no experience at all (or whatsoever) about differentiating vectors. I am at a total loss here. I even have no idea regarding the difficulty of this (thus the [ I ] prefix). Please help me.

How did the two equations below come out? Can someone show me formulas on how did these appear? What happened to the ^T?

I did search for resources over the net about formulas and I got even more confused.

The bolded variables are matrices... or vectors. I think.

View attachment 195869

It seems to me that A and V^-1 are square matrices, and that $y, \hat{y}$, and $\lambda$ are vectors of a suitable size to make the multiplication operation defined.
To get $\frac{\partial J}{\partial \hat y}$, they used the product rule for the first term, what amounts to the constant multiple rule for the second term. After this, it appears that they then did some simplification to get their answer into the form you show.
To get $\frac{\partial J}{\partial \lambda}$, they differentiated $-2\lambda^TA\hat y$, which would result in $-2A\hat y$.
Further, it appears to me that both partials were then set to 0.