# Latex math commands I have newly learned or consistently forget

15 Feb 2022This post is mainly written for me – I’m in the flow of writing something, and … have to look up how to typeset an equation. Uggh. So here’s some of the math commands I either learned for the first time, or always forget.

First, a good guide is the “short Math Guide for Latex” from the American Mathematical Society:

### Approximately

`\approx`

\(\quad \approx\)

### Big slashes for division

Use the left-middle-right construct. Relevant StackOverflow answer.

`\left. \frac{a}{b} \middle/ \frac{c}{d} \right.`

\(\quad \left. \frac{a}{b} \middle/ \frac{c}{d} \right.\)

### Labeling matrix rows and columns

I needed something that would work with MathJax. A simple version of the below – and how I got it working!- is due to this blog post. If you’re working with modern latex (versus MathJax), Shanto Roy’s post on this topic has a lot of options and detail.

```
\begin{array}{c c c c c} &
\begin{array}{c c c c} n & m_1 & m_2 \\
\end{array}
\\
\begin{array}{c}
n \\
m_1\\
m_2
\end{array}
&
\left[
\begin{array}{c c c}
0 & A^T & B^T \\
A & I & 0 \\
B & 0 & 0
\end{array}
\right]
&
\left[
\begin{array}{c}
x \\
r\\
\lambda
\end{array}
\right]
&
=
&
\left[
\begin{array}{c}
0\\
b\\
d
\end{array}
\right]
\end{array}
```

to

\[\begin{array}{c c c c c} & \begin{array}{c c c c} n & m_1 & m_2 \\ \end{array} \\ \begin{array}{c} n \\ m_1\\ m_2 \end{array} & \left[ \begin{array}{c c c} 0 & A^T & B^T \\ A & I & 0 \\ B & 0 & 0 \end{array} \right] & \left[ \begin{array}{c} x \\ r\\ \lambda \end{array} \right] & = & \left[ \begin{array}{c} 0\\ b\\ d \end{array} \right] \end{array}\]A simpler version – from the blog post above – is

```
\begin{array}{c c} &
\begin{array}{c c c} a & b &c \\
\end{array}
\\
\begin{array}{c c c}
p \\
q\\
r
\end{array}
&
\left[
\begin{array}{c c c}
.1 & .1 & 0 \\
.4 & 1 & 0 \\
.8 & 0 & .4
\end{array}
\right]
\end{array}
```

### Argmin

To get something like this,

\[\DeclareMathOperator*{\argmin}{arg\,min} SVDO(A) = \argmin_{\mathbf{R} \in O(n)} \| \mathbf{R} - \mathbf{A} \|_F^2 \label{SVDO}\]Do something like this in your .tex file.

```
\DeclareMathOperator*{\argmin}{arg\,min}
SVDO(A) = \argmin_{\mathbf{R} \in O(n)} \| \mathbf{R} - \mathbf{A} \|_F^2 \label{SVDO}
```

Relevant StackExchange answer.

### Input versus Include

I was using `\include{file}`

and that didn’t work. To import everything from a file, I need to use `\input{file}`

.

More details from this SE answer.

### Defining long expressions in the preamble

I always use boldface for vectors and matrices. That means a WHOLE LOTTA `\mathbf{A}`

, missing brackets, etc.

Instead, I’m trying this out:

```
\DeclareMathOperator{\A}{\mathbf{A}}
...
$\A$
```

To get \(\DeclareMathOperator{\A}{\mathbf{A}} \A\).

A detail: On page 13 of the AMS short math guide, pdf, there is an explanation of when to use and asterisk versus not:

The star form \DeclareMathOperator* creates an operator that takes limits in a displayed formula, such as sup or max.

So if the expression does not have limits, use `\DeclareMathOperator{\A}{\mathbf{A}}`

, otherwise `\DeclareMathOperator*{\argmin}{arg\,min}`

.

### Horizontal spacing in math expressions

My previous post about this.

### Local font size changes

```
\Huge
\huge
\LARGE
\Large
\large
\normalsize
\small
\footnotesize
\scriptsize
\tiny
```

See LaTeX-Tutorial.com’s post for more information.

### Norm marks that are sized to the content

In LaTeXese, this is *responsive* sizing.

You can do

```
\left\lVert Thing to be normed \right\rVert
```

Or as Jidan at physicsread.com suggests, you can create a command

```
\newcommand\norm[1]{\left\lVert#1\right\rVert}
...
$\norm{Thing to be normed}$
```

I linked to the particular section about responsive resizing from the post above, but the whole page is all about how to do norms in latex and was useful to me.