LaTeX Math I often use

Logical operators

Info

Logical operators in LaTeX typically are l[name], like \lnot, \land, etc.

$$
\lnot (A \land B) \iff \lnot B \lor \lnot A \quad \text{(De Morgan’s law)}
$$

$$\neg (A\wedge B)⟺\neg B\vee \neg A\text{(De Morgan’s law)}$$

Mid for probabilities and sets

$$
Pr(x \mid y) = \frac{Pr(y \mid x) Pr(x)}{Pr(y)} \quad \text{(Bayes theorem)}
$$

$$Pr(x\mid y)=\frac{Pr(y\mid x)Pr(x)}{Pr(y)}\text{(Bayes theorem)}$$

$$
X = \{(y,z) \mid y \in Y, z \in Z \} \quad \text{(Cartesian Product)}
$$

$$X=\{(y,z)\mid y\in Y,z\in Z\}\text{(Cartesian Product)}$$

Norm of matrix or vector

$$
\| x \|^2
$$

$$\Vert x{\Vert }^2$$

Multi-line equations

Info

use & before operator (e.g., =) to make equations line up at them, and \\ for new lines. quad provides space between math on the same line, which can be useful for putting \text{} on the right side

$$
\begin{aligned}
1 + 2 + 3 &= 7 - 1 \quad \text{(This is true)} \\
10 &= 10 \quad \text{(Also true!)}
\end{aligned}
$$

$$\begin{array}{rl}1+2+3& =7-1\text{(This is true)}\\ 10& =10\text{(Also true!)}\end{array}$$

Making column vectors and row vectors

Info

Use vdots and ldots for 3 dots to be rendered vertically and horizontally, respectively.

$$
\begin{bmatrix}
x_1 \\
\vdots \\
x_n \\
\end{bmatrix}
$$

$$\left[\begin{array}{c}{x}_1\\ ⋮\\ x_n\end{array}\right]$$

$$
[x_1, \ldots, x_n]
$$

$$[x_1,\dots ,x_n]$$