Matrix Derivation: 2x1 A and B with Dimension and dA/dB Calculation

[tommyhakinen]

Hi,

I need help with matrix derivation. I have 2 matrices of dimension 2x1, A and B.
A = [f(x) x]$$^{T}$$
B = [y x]$$^{T}$$

I would like to find the dA/dB. How do I do this? and what is the dimension of the resultant matrix?

 

[Fredrik]

What is the function that you want to take the derivative of?

 

[batboio]

$$\frac{D(A)}{D(B)}=\left(\begin{array}{cc}\frac{\partial f(x)}{\partial y}&\frac{\partial f(x)}{\partial x}\\\frac{\partial x}{\partial y}&\frac{\partial x}{\partial x}\end{array}\right)=\left(\begin{array}{cc}0&f^\prime\\0&1\end{array}\right)$$

This should be it if I'm not mistaken. What you're asking is basically the Jacobian matrix of a vector-valued function $$g(y,x)=(f(x),x)$$

 

[tommyhakinen]

$$\frac{D(A)}{D(B)}=\left(\begin{array}{cc}\frac{\partial f(x)}{\partial y}&\frac{\partial f(x)}{\partial x}\\\frac{\partial x}{\partial y}&\frac{\partial x}{\partial x}\end{array}\right)=\left(\begin{array}{cc}0&f^\prime\\0&1\end{array}\right)$$

This should be it if I'm not mistaken. What you're asking is basically the Jacobian matrix of a vector-valued function $$g(y,x)=(f(x),x)$$

thank you very much. that helped a lot.

 

[naghmeh_ms]

please help me about this quastion :
suppse A be a square matrix and X be a coln matrix AT and XT are their transpos matrices find a formula for this derivative :
d XTATAX/ dA

 

[micromass]

Please create a new thread for your question. And if it is homework, it belongs in the homework forums.