# Thread: vector valued function

1. ## vector valued function

For the vector valued function F = (x^2-y^2)i + 2xyj,

how do I find the matrix for the gradient of F?

2. If ${\bf F}(x,y)=f_1(x,y){\bf i}+f_2(x,y){\bf j}$, then

$\nabla {\bf F}=\left(\begin{array}{cc} \partial_x f_1 & \partial_y f_1 \\ \partial_x f_2 & \partial_y f_2 \end{array}\right)$

where

$\partial_x f=\frac{\partial f}{\partial x}$ etc.

3. I don't really understand your notation.

Is the matrix easy to set up?

Could you explain in a little more detail?

Would the matrix be
2x -2y
2y 2x ?

4. Originally Posted by Adebensjp05

Would the matrix be
2x -2y
2y 2x ?
Yes!