# Which “bold” style is recommended for matrix notation?

I am wondering which "bold"-style is the "appropriate" or "official" way for matrix notation. E.g., let's say the matrix "A." \textbf{A} would result in a more italics representation compared\textbf{A} etc.

• \boldsymbol{A}
• \textbf{A}
• \pmb{A}
• \boldmath{A}
• You would probably get at least 4 answers with this question; one for each of the options listed. As such, even though the request includes a reference to "official", it's seems primarily opinion-based. – Werner Sep 6 '14 at 7:03
• Haha, Sebastian. Just now I've noticed we had the same question. It's curious how alike people keep meeting each other "by accident" again and again. Nevertheless, you didn't follow the ISO/IEC in your book ;) – Atcold Jul 26 '16 at 15:09
• @Atcold Haha, yeah that's right, but only half of the story :P. I followed the standard in my drafts (converted my markdown/latex docs to Word so that the editors would accept them) ... And eventually, their layout team re-typed (or let's say they had to "redraw") the equations (they were not used to having equations and their layout software couldn't handle them). – user34074 Jul 27 '16 at 23:05

ISO/IEC regulations for technical writing prescribe using bold italic for matrices (and slanted sans serif for tensors). I find these regulations incoherent, but if you work in some fields you are required to follow those regulations. Why incoherent? From a mathematical point of view, a matrix is a tensor.

On the other hand, pure mathematics and theoretical physics mostly ignore those regulations. Doing pure mathematics, I'd not use any special notation for matrices, that are just another mathematical object which a variable is assigned to. For undegraduate textbooks, a special notation is usually employed, in order to help students find their way; upright boldface is mostly used.

Now to the TeXnical part. First of all you should define a personal command:

\newcommand{\matr}[1]{\mathbf{#1}} % undergraduate algebra version
%\newcommand{\matr}[1]{#1}          % pure math version
%\newcommand{\matr}[1]{\bm{#1}}     % ISO complying version


and use \matr (any other name is possible, of course). This will allow changing just the definition instead of chasing in the document in case you change your mind about the problem.

Note that \boldsymbol (from amsbsy) is obsolete and \bm (package bm) should be used.

Don't use \textbf, because this will inherit font settings from the context, so in a theorem statement you'd get bold italic.

Never ever use \pmb (unless you're in an emergency with some symbol for which there's no other bold version). The syntax \boldmath{A} will do nothing else than issuing two warnings and typeset a normal math italic “A”.

See Consistent macro for bold upright vectors in both latin and greek in case you need also Greek letters for matrices.

About amsbsy and \boldsymbol being obsolete, here's the start of the manual for amsbsy:

• @egreg: would you mind adding a citation for your "\boldsymbol is obsolete" statement? Thank you. – Atcold Jul 26 '16 at 14:48
• @Atcold Just look at the documentation for amsbsy; I added a screen shot of the first page. – egreg Jul 26 '16 at 14:52
• One more question. You mentioned the ISO/IEC regulations... is there a reference for that as well? I personally like my vector bold and crooked (it was meant to be a joke as well, anyhow bold-italic). But, what does the ISO/IEC regulations say about them? Thank you again. – Atcold Jul 26 '16 at 15:16
• @Atcold The ISO standard is number 80000-2:2009 that has superseded ISO 31-11. What these standards say precisely I don't know; partial descriptions are available on the net, but I'm not wanting to pay in order to know how I'm supposed to write mathematics. I can just look at mathematical books and articles, where math is written mostly in disagreement with ISO. Am I being polemic? Yes, I am. If you are compelled to adhere to the ISO standard, obey; if you want to write real mathematics, use the way that has been common for a couple of centuries before ISO was even created. – egreg Jul 26 '16 at 15:41
• Haha, OK, fair enough. That's way too much money. This stuff should be open source and community based. Thank you for your time, btw. :) – Atcold Jul 26 '16 at 15:53

I honestly don't think there is an official bold typeface for matrices. It is rather an inherited typographical convention from the nineteenth century, when put fashion boldface, arise matrices and vectors and in the absence of typefaces that could easily and properly represent the arrows on the vectors, these and matrices are typeset in bold since then.

I can't assure you that the visual result of the four options you mention is identical, however, the only thing required by this convention is that the name of the matrix will be compound with bold and uppercase letters, regardless of how you get it.

• You might like to add a comment that it is always best to create a new macro for such things, e.g. \newcommand*{\matrix}[1]{\mathbf{#1}}, to keep in line with consistent typography; so it is very easy to change one's mind about the particular style of matrix representation. – moewe Sep 6 '14 at 8:19
• You might also want to consider the difference between \textbf and \mathbf (see Why Different Commands for Seemingly Similar Tasks? and this answer or this): \textbf{A_1} will not work, but \mathbf{A_1} will. You might also want to mention the bm package \bm package versus \boldsymbol and Bold math: .... – moewe Sep 6 '14 at 8:21
• As an orthogonal comment, I never see a matrix in bold in linear algebra context but whenever I read fluid mechanics or similar fields which utilize matrices in a rather not-so-much fashion, use this bold notation. I agree that tradition runs strong on those fields. – percusse Sep 6 '14 at 9:25
• Thanks @moewe for the comments, I was almost asleep when answered, so I left out all those details that egreg forth in a very clear way. – Aradnix Sep 6 '14 at 16:58
• Let me clarify what I mean; if say a field is using the matrices as a shorthand over index notation, they tend to treat matrices as special objects which is nothing but tradition. However if a research field is using manipulations matrices just as any other objects, they get away without bolds, italics etc. since there is a strong affinity among the peers. Hence they don't need an extra roadsign that screams look at me I'm a matrix. – percusse Sep 7 '14 at 1:27

Applied mathematics, particularly, abounds with long complicated expressions whose basic variables are scalars, (column) vectors, and matrices. To give immediate visual insight into the structure of these expressions, it is useful to maintain a consistent typographical convention to distinguish the three types of variable. This is because the kinds of manipulation that can be performed on each type are different, especially those involved in chains of equalities needed to get a particular result. For example, we may be able to take out of an expression a (square nonsingular) matrix factor, because such a matrix can be inverted; while it would make no sense to "invert" a vector.

A good convention is to use lowercase italic for scalars, lowercase bold italic for vectors, and capital italic for matrices, and similarly for scalar/vector/matrix-valued functions. If it is necessary to use both lowercase and capitals for scalars, then capital bold italic can serve for matrices. The reason for preferring italic for variables is that roman (upright) type signals a term with standard constant meaning, where juxtaposition is a feature of spelling rather than an indicator of multiplication.

• This convention would be utterly unreadable for example in convex optimization or similar fields. And tedious too since we are exclusively dealing with matrices or vectors. Capital for matrices and lowercase letters for vectors serves as good as any other with no exception. Invertibility should either be assumed or proved so it's authors' responsibility to present the context clearly not the readers'. – percusse Sep 7 '14 at 1:22