Derivative of a Matrix with respect to a vector

linear-algebra calculus matrices derivatives

A natural definition is $$\frac{\partial {\textbf A}}{\partial {\textbf x}}={\textbf C}$$ where C is a 3D matrix (or tensor) with $$C_{n,m,\ell}=\frac{\partial A_{n,m}}{\partial x_\ell}$$

The order of the subindexes is open to different conventions, of course.

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