0

Let

$$ f(x, y) = \begin{pmatrix} h_{1}(x, y) & h_{2}(x, y) \end{pmatrix} \begin{pmatrix} h_{1,1}(x, y) & h_{1,2}(x, y) \\ h_{2,1}(x, y) & h_{2,2}(x, y) \end{pmatrix}^{-1} \begin{pmatrix} k_{1} \\ k_{2} \end{pmatrix}. $$ I want to calculate its partial derivatives $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$. The problem I have concerns the derivative of the inverse matrix. How can I do that?

Any suggestions will be appreciated.

R. Ho
  • 1
  • http://math.stackexchange.com/questions/190424/how-to-evaluate-the-derivatives-of-matrix-inverse – Intelligenti pauca Aug 24 '16 at 09:06
  • IMHO, it is not worth the value to stay with matrix notations in such a low dimensional case : your function is nothing else than : $\dfrac{k_1(h_1h_{22}-h_2h_{21})+k_2(h_2h_{11}-h_1h_{22})}{D}$ where $D:=h_{11}h_{22}-h_{21}h_{12}$ – Jean Marie Aug 24 '16 at 09:20

0 Answers0