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I need to apply a differential operator (nabla) on a matrix. Problem is, that I don't know how to calculate that. Do I treat nabla as a column vector and simply multiply vector with the matrix? Or is nabla to be handled as jacobi matrix?

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    Treat it the same as a vector function, just with the entries in a different arrangement.2012-08-23

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The differential operators can be defined in a matrix of differential operators, so that, for instance, it could be applied to a matrix containing n vectors, one in each column.

$ \left[\begin{matrix} \frac{\partial}{\partial{x}} & \frac{\partial}{\partial{y}} & \frac{\partial}{\partial{z}}\\ \end{matrix}\right] \left[\begin{matrix} x_1 & x_2 & x_3 & & x_n \\ y_1 & y_2 & y_3 & \dots & y_n \\ z_1 & z_2 & z_3 & & z_n \\ \end{matrix}\right] $

To see how to implement this kind of operator in the Python mudule Sympy, you can refer to here. To see more discussion about matrix of differential operator, see here.