Can a matrix have partial derivatives?

Question

Consider a 2 dimensional matrix $A$ with dimensions $n \times n$.

Can I calculate the partial derivatives of this matrix? i.e. $\frac{\partial A}{\partial x}$ and $\frac{\partial A}{\partial y}$.

Obviously using finite differences, but I want to know whether it's correct to calculate partial derivatives of a matrix.

Thanks.

Answer 1

Sure. After all, you can think of a matrix as a vector, or better vector valued function, with length $n^2$. Then proceed taking partial derivatives as you would for a vector field.