matrices

$ \begin{matrix} A_11 & A_12 & \cdots & A_{1m} \\ A_21 & A_22 & \cdots & A_{2m} \\ \vdots & \vdots & \ddots & \vdots \\ A_{n1} & A_{n2} & \cdots & A_{nm} \end{matrix} $

The above undecorated matrix is generated with:

\begin{matrix}
A_11 && A_12 & \cdots & A_{1m} \\
A_21 && A_22 & \cdots & A_{2m} \\
\vdots & \vdots & \ddots & \vdots \\
A_{n1} & A_{n2} & \cdots & A_{nm}
\end{matrix}

We can add brackets either by using \left or \right or by replacing matrix with:

pmatrix $\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}$

bmatrix $\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$

Bmatrix $\begin{Bmatrix}1 & 2 \\ 3 & 4\end{Bmatrix}$

vmatrix $\begin{vmatrix}1 & 2 \\ 3 & 4\end{vmatrix}$

Vmatrix $\begin{Vmatrix}1 & 2 \\ 3 & 4\end{Vmatrix}$.

braket

$\langle{x}\rvert$

$\lvert{x}\rangle$

$\langle{a}\mid{b}\rangle$