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Math Help - vector valued function

  1. #1
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    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?
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  2. #2
    Super Member Rebesques's Avatar
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    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.
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  3. #3
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    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 ?
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  4. #4
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    Quote Originally Posted by Adebensjp05 View Post

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