This article is aimed at relatively new 
1. New Paragraphs
In
Do not start a new paragraph by using \\ (it merely terminates a line). Indeed you should almost never type \\, except within environments such as array, tabular, and so on.
2. Math Mode
Always type mathematics in math mode (as $..$ or \(..\)), to produce “
$$, \[..\], or one of the display environments (see Section 7).
Punctuation should appear outside math mode, for inline equations, otherwise the spacing will be incorrect. Here is an example.
- Correct:
The variables $x$, $y$, and $z$ satisfy $x^2 + y^2 = z^2$. - Incorrect:
The variables $x,$ $y,$ and $z$ satisfy $x^2 + y^2 = z^2.$
For displayed equations, punctuation should appear as part of the display. All equations must be punctuated, as they are part of a sentence.
3. Mathematical Functions in Roman
Mathematical functions should be typeset in roman font. This is done automatically for the many standard mathematical functions that \sin, \tan, \exp, \max, etc.
If the function you need is not built into amsmath package and type, for example,
\usepackage{amsmath}
...
% In the preamble.
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\inert}{Inertia}
Alternatively, if you are not using the amsmath package you can type
\def\diag{\mathop{\mathrm{diag}}}
4. Maths Expressions
Ellipses (dots) are never explicitly typed as “…”. Instead they are typed as \dots for baseline dots, as in $x_1,x_2,\dots,x_n$ (giving 
\cdots for vertically centered dots, as in $x_1 + x_2 + \cdots + x_n$ (giving 
Type $i$th instead of $i'th$ or $i^{th}$. (For some subtle aspects of the use of ellipses, see How To Typeset an Ellipsis in a Mathematical Expression.)
Avoid using \frac to produce stacked fractions in the text. Write 
For “much less than”, type \ll, giving 
<<, which gives 
\gg, giving 
\langle and \rangle:
- incorrect: <x,y>, typed as
$<x,y>$. - correct:
, typed as
$\langle x,y \rangle$
5. Text in Displayed Equations
When a displayed equation contains text such as “subject to 
\mathrm put the text in an \mbox, as in \mbox{subject to $x \ge 0$}. Note that \mbox switches out of math mode, and this has the advantage of ensuring the correct spacing between words. If you are using the amsmath package you can use the \text command instead of \mbox.
Example
$$
\min\{\, \|A-X\|_F: \mbox{$X$ is a correlation matrix} \,\}.
$$
6. BibTeX
Produce your bibliographies using BibTeX, creating your own bib file. Note three important points.
- “Export citation” options on journal websites rarely produce perfect bib entries. More often than not the entry has an improperly cased title, an incomplete or incorrectly accented author name, improperly typeset maths in the title, or some other error, so always check and improve the entry.
- If you wish to cite one of my papers download the latest version of
njhigham.bib(along withstrings.bibsupplied with it) and include it in your\bibliographycommand. - Decide on a consistent format for your bib entry keys and stick to it. In the format used in the Numerical Linear Algebra group at Manchester a 2010 paper by Smith and Jones has key
smjo10, a 1974 book by Aho, Hopcroft, and Ullman has keyahu74, while a 1990 book by Smith has keysmit90.
7. Spelling Errors and Errors
There is no excuse for your writing to contain spelling errors, given the wide availability of spell checkers. You’ll need a spell checker that understands
There are also tools for checking lacheck, which describes itself as “a consistency checker for LaTeX documents”. Such a tool can point out possible syntax errors, or semantic errors such as unmatched parentheses, and warn of common mistakes.
8. Quotation Marks
\lq, and a right quotation mark, denoted here \rq, typed as the single left and right quotes on the keyboard, respectively. A left or right double quotation mark is produced by typing two single quotes of the appropriate type. The double quotation mark always itself produces the same as two right quotation marks. Example: 
\lq\lq hello \rq\rq.
9. Captions
Captions go above tables but below figures. So put the caption command at the start of a table environment but at the end of a figure environment. The \label statement should go after the \caption statement (or it can be put inside it), otherwise references to that label will refer to the subsection in which the label appears rather than the figure or table.
10. Tables
\cline, \hline, and the | column formatting symbol. However, it is good style to minimize the number of rules. A common task for journal copy editors is to remove rules from tables in submitted manuscripts.
11. Source Code
Example:
Good:
$$
U(\zbar) = U(-z) =
\begin{cases}
-U(z), & z\in D, \\
-U(z)-1, & \mbox{otherwise}.
\end{cases}
$$
Bad:
$$U(\zbar) = U(-z) =
\begin{cases}-U(z), & z\in D, \\
-U(z)-1, & \mbox{otherwise}.
\end{cases}$$
12. Multiline Displayed Equations
For displayed equations occupying more than one line it is best to use the environments provided by the amsmath package. Of these, align (and align* if equation numbers are not wanted) is the one I use almost all the time. Example:
\begin{align*}
\cos(A) &= I - \frac{A^2}{2!} + \frac{A^4}{4!} + \cdots,\\
\sin(A) &= A - \frac{A^3}{3!} + \frac{A^5}{5!} - \cdots,
\end{align*}
Others, such as gather and aligned, are occasionally needed.
Avoid using the standard eqnarray, because it doesn’t produce as good results as the amsmath environments, nor is it as versatile. For more details see the article Avoid Eqnarray.
13. Synonyms
This final category concerns synonyms and is a matter of personal preference. I prefer \ge and \le to the equivalent \geq \leq\ (why type the extra characters?).
I also prefer to use $..$ for math mode instead of \(..\) and $$..$$ for display math mode instead of \[..\]. My preferences are the original 
I don’t think many people use
\begin{math}..\end{math}
or
\begin{displaymath}..\end{displaymath}
Also note that \begin{equation*}..\end{equation*} (for unnumbered equations) exists in the amsmath package but not in in
and 
, was first introduced in the programming language 
and 
in the context of groups, but both were ungainly and difficult to typeset. In 1928, Hensel suggested the notation 
and 
. Although his suggestion appears to have attracted little or no attention, it was was reinvented by Cleve Moler for MATLAB and is now a notation familiar to anyone who works in numerical linear algebra.
, where 
is a 3-by-
is an 
is possible for different vectors 
and 
. This equation is equivalent to saying that 
for a nonzero vector 
, or, in other words, that a matrix with fewer rows than columns has a nontrivial null space.
Nick Higham 