|Matrices and tensors can be written in bold capital, sans serif, double underarrow/double underscore/whatever, the list could go on and on depending on the author's preference. I am not saying sans serif should become dominant in WP, and that all sources use sans serif, again it’s only an alternative font for editors to use in the odd cases when different fonts are used.
Obviously we can't use sans serif all the way through an article (unless LaTeX is not used). Given that we should use the same notation styles in the literature, this should not be done anyway, so people can and should just use the defualt fonts in the LeTeX rendering. I would suggest that in Wikipedia:Manual of Style/Mathematics#Notational conventions we write something along these lines, if there is much request for usage of sans serif.
- Vectors: capital or lowercase, plus underline (perhaps for tuples)
or arrow/bold (for "geometric/physical" vectors/vector fields associated with a direction):
of course either case is usual and interchangeable. However sources also use lowercase sans serif for row/column vectors:
so I don't know if people would use this in conjunction with sans serif matrices...
- Matrices/dyadics/2nd order tensors: capital and bold
or bold/non-bold sans serif
(presumably the former may be preferable). The exceptions to these are if the context simply uses italics as though they were scalars (see the Dirac matrices in the Dirac equation or Pauli matrices ).
- Tensors in general: use bold sans serif, as in
rather than just bold or bold-italic , and not blackboard bold... as currently used in the Navier–Stokes equations:
which could be written:
- Standard sets: (real, complex numbers etc) use blackboard bold as usual: , rather than ordinary bold as sometimes used, which would be reserved for vectors/matrices.
In this way, ambiguity is prevented, since
- The lower case "l" (ell) for (say) a vector will not be in sans serif, but usual serif (and preferably curly) , or even .
- The identity operator/matrix written as next to other letters should not be confused for a vertical bar such as , also . For statements like:
in tensors in curvilinear coordinates, it should be clear that " is the identity map" is not a "misplaced bar" (or whatever): ...
- Tensor equations (without resort to indices) can be written
where the first may be confused for a vector equation, the second is less obvious for which quantities are vectors or tensors for someone who doesn't know. (The equations should obviously be clarified in the context anyway, but the notation may appear inconsistent for some, and it would be more obvious and followable for the reader if bold serif was for vectors, bold sans serif for tenors).
Anyway that's how I propose to use sans serif with everything else, if used at all... I will not use it myself, unless this becomes accepted (so to speak, even then only very occasionally).