# Conventions for typesetting complex vectors and vectors with complex components

I was wondering if there were conventions for typesetting vectors and complex numbers.

I grew up in France and I'm used to putting an arrow on my vectors ($\vec{v}$) and a bar on my complex numbers ($\bar{z}$) when the variable type is not obvious.

This page on the LaTeX wikibook suggests using a bold font for vectors. I think I have seen that used in textbooks too. What about complex numbers? And vectors with complex coordinates? Are there any conventions there?

To answer your question: there is no single answer. Even at our Mathematics department, for the first grade students, there are two professors of linear algebra, one uses $\bm{v}$ (bold math from bm package), the other one uses $\vec{v}$.

I would not use bar for complex numbers, because $\bar{z}$ often denotes the conjugate of $z$. I think that you should always make clear in the text whether you are real or complex.

Generally: In my opinion, you can use whichever notation you want, as far as you use it consistently in the whole work, and make clear (in Table of Notations in the Preface, or in the Introduction) what notation you use.

• Tell the first one to use \bm{v} from the bm package, as \boldsymbol is considered obsolete. Commented Jan 30, 2012 at 15:33
• I tend to use \mathbf, actually; but ISO norms prescribe the equivalent of \bm Commented Jan 30, 2012 at 15:46
• @egreg I've never liked upright letters in mathematics, and especially things like $u mathbf{v}$ look really bad and i need it quite a lot.
– yo'
Commented Jan 30, 2012 at 15:52
• I changed my newcommand \vect to have \newcommand{\vect}[1]{\bm{#1}}. I like that bm gives me both bold and italic, as indeed the upright letters were itching me. Commented Jan 31, 2012 at 9:36
• @egreg Could you please specify which ISO norm prescribes the use of \bm? There is no information on the complex number typesetting in ISO 80000 that I usually use. Commented Mar 18, 2023 at 14:56

Even though I hardly relate this question to TeX fora it is still a question of high importance in the field.

It doesn't even seem fit on sister site Math StackExchange

And some kinds of questions are considered off-topic:

• Typesetting equations

Even though they refer to here...

In general there is no applicable convention. You are free to use what ever you see fit.

## Bold method

I have always used the bold type. Not only have I encountered this in the majority of my learning books, I also think that it seams fit to use that convention. It is short and concise, yes, in some cases it can be hard to see the difference if all variables are vectors, but you cant clarify everything for the reader.

## Arrow method

The arrow I don't like. Most of all due to the complexity of writing a vector transposed, or maybe a vector to the second power and then transposed. The more you stack on top, the uglier it gets... In my opinion.

## Complex numbers

Complex numbers I just usually denote with z or c which in typical school books are used as complex values. There is to my knowledge no standard on typesetting complex numbers. Just denote it by \in\mathbb{C}.

Complex vectors I handle the same as real vectors.

As has been said, the main thing is that you need to be consistent! This is the most important thing.

• Interesting that since ever I have used \mathbb{C},\mathbb{R} for fields.
– yo'
Commented Jan 30, 2012 at 15:42
• sorry I had just used that for numerous mathematical notation.! Commented Jan 30, 2012 at 15:55