# Recommendations for markup of vectors and matrices

Up to now I was used to denote vectors by bold italic symbols and matrices by upright bold symbols. Now that I learned that by the norm ISO-80000 also matrices should be written using italic letters, I am wondering what might be the best way to distinguish these quantities. Normally matrices and vectors are denoted by capital and lower case letters, respectively. But in my case I need to use also capital letters for vectors (in body coordinates) and lower-case letters for matrices (infinitesimal rotation matrices in space coordinates). Another possibility would be to use greek letters for quantities in body coordinates. But several capital greek letters look identical to their latin counterparts and I would not like to frighten the undergraduate students. I would also like to avoid additional left or right sub- or superscripts. For the slides I had also some trouble with designing \Omega matrices and their corresponsing vectors, because I didn't yet manage to find bold italic greek letters; so at the moment I simply use blue symbols for these. I would be happy about all suggestions; for this semester I will probably stick with my old convention in order to avoid too much confusion. With kind regards Alois

• I've seen long ago matrices denoted in a sans font. – Bernard Oct 12 '20 at 18:11
• note that ISO-80000 is mostly for mathematics as used by a sector of engineering disciples, it doesn't really apply to mathematical typesetting as used in mathematics. – David Carlisle Oct 12 '20 at 22:15

I don't know much about typographic conventions, so I don't know how much this answer can be useful, but I had similar issues and after looking around and also asking here, I find very useful to indicate all kind of vectors with bold letters, as you said, so for example \boldsymbol{x},\boldsymbol{A}, while for matrices I use the commands \mathbb and \mathb  (non-standard, explained in the following).

You may check this question that I asked some weeks ago, that received truly amazing answers. The author of the principal one defines this new \mathbb command, but I simply redefined it \mathb to still be able to use the original \mathbb; in that way you should be able to write for example \mathb{\sigma} for sigma matrices, thing that is absolutely impossible with the standard \mathbb.

Also notice that for example \mathbb{A},\mathb{A} have quite different appearances so they can be used with different meanings; at the same time you are able to create e.g. a vector of matrices, such as \vec{\mathb{\sigma}}, thing that would become really annoying with other conventions, such as when you put an hat on matrices. You would write \vec{\hat{A}} and you would have a lot of vertical spacing issues; also writing \norm{\hat{A}} (\norm defined is physics package) is a true pain (I asked also about this and received great answers for this problem too, but the hat convention has its limits, according to my opinion).

That's my experience and my conventions, that I was able to use thanks of great people here.

Just try different things and let me know if this can be helpful. Greetings, Rob.

Since vectors are merely rank one tensors, I usually just notate them as tensors. There must obviously be some changes and compromises because too many sources (authors and textbooks) are not consistent with notation and too many authors scoff at the ISO recommendations. Therefore, you are unlikely to find consensus here. Don't be afraid to adopt your notation as you see fit for the benefit of your students.

• It isn't that people scoff at the ISO, but ISO isn't a monolithic organisation making global recommendations it's an umbrella organisation in which individual groups can get standards for specific things. ISO:80000-2 is almost entirely for mathematics as used in engineering. It does not describe or standardise mathematical typesetting as used in mathematics. The Office XML format used by Word is also an ISO standard (ISO/IEC 29500) but that does not mean you should stop using tex and use Office. – David Carlisle Oct 12 '20 at 22:21