math-modetypographyvector
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?
Consistency is the primary goal. So the first task is to know what "special numbers" we need and define commands for them:
\newcommand{\euler}{e}
\newcommand{\ramuno}{i}
(ramuno was how some Italian mathematicians of the 16th century called the quantity that squared gives –1; then Euler started using i).
The mathematical typography tradition usually didn't have a special treatment of these symbols. See, for example, n. 359 in Gauss's Disquisitiones Arithmeticae, where the equivalent of
$\cos\frac{\lambda kP}{e} + i\sin\frac{\lambda kP}{e}$
is found (the edition I consulted is from the Werke by the Königlichen Gesellschaft der Wissenschaften in Göttingen, vol. 1, 1863, page 450). There's no doubt what this i is denoting.
http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235993352&IDDOC=137206
However, in recent times, under the influence of physics and applied mathematics, people started to denote "constants" with upright letters. There's even an ISO regulation about this, which is compulsory in some fields where uniformity among papers and books is very important.
In pure mathematics there's essentially no rule. Do as you like or how your field is used to. Using special names for the special numbers allow you to change the appearance of your document just by changing the definition.
If you feel that there may be confusion between the "imaginary unit" (no worse name could be chosen for it) and an index (for summations, for instance), you have three strategies:
use a special denotation for the imaginary unit;
don't use i as an index;
forget about it and let the reader know from the context.
Strategy 2 is used by Graham, Knuth and Patashnik in their "Concrete Mathematics". Strategy 3 is very common in math textbooks.
The steinmetz package was written exactly for this.
\documentclass{article}
\usepackage{steinmetz}
\begin{document}
$z = 1.19 \phase{-78.2039^{\circ}}$
\end{document}
Best Answer
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 frombmpackage), 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.