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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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    I've never seen the standard *del* operator $\nabla$ applied to a matrix. What is the context of the application?2012-08-23
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    There isn't really any difference between the $\nabla$ and Jacobi-matrix (up to transposition), it only depends on where your function, defined on matrices, maps to.2012-08-23
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    It depends on what you mean by applying a differential operator to a matrix. What kind of entries does the matrix have? What do you want this differential operator to do to it?2012-08-23
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    Context is the nonlinear sigma model in quantum field theory, where I want to use a matrix function $\phi$ instead of a vector function. The matrix is a 3x3 one with simple scalar functions in it.2012-08-23
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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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