Derivations and matrices
The discussion which is exposed in the document wants to bring another manner to envisage derivations acting on vectors. More precisely, it focuses on the fact that some derivations may be represented with matrices.
The initial motivation for this essay lies on an intuitive belief. Let me develop. The concept of derivation is far to be new. It started a few centuries ago with the efforts of well-known people like Descartes or Leibniz. A part of the derivations concerning numerical functions can concretely be realized (I mean calculated) only because we dispose of a whole set of formula.
We know that the components of vector fields are sometimes numerical functions; we have fantastic computers and programmers. This give rise to the intuitive idea that derivations concerning these vector fields might be done with the help of algorithms.
Since it is more economic to calculate anything with the help of matrices, we ask if some of these derivations acting on vector fields can be represented by matrices? And we bet that a positive answer may help people working in diverse domains of physics (e.g.: aeronautics, hydrodynamics, etc.).
The first version of this document has been presented in March 2021; sometimes in two parts. This version is a re-looking of the first one. There is no fundamental difference, but the redaction has been re-worked to make the understanding easier. The immature sections have been eliminated.
Characteristics of the document
It could be useful to read this document as a complement for the discussion concerning the formalism of the electromagnetic field tensor.