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Matrices

No delimiters

$$
\begin{matrix}
  x_{11} & x_{12} \\
  x_{21} & x_{22}
\end{matrix}
$$

Parenthesis

$$
\begin{pmatrix}
x_{11} & x_{12} \\
x_{21} & x_{22}
\end{pmatrix}
$$

Bracketed

$$
\begin{bmatrix}
x_{11} & x_{12} \\
x_{21} & x_{22}
\end{bmatrix}
$$

Braces

$$
\begin{Bmatrix}
x_{11} & x_{12} \\
x_{21} & x_{22}
\end{Bmatrix}
$$

Vertical bars

$$
\begin{vmatrix}
x_{11} & x_{12} \\
x_{21} & x_{22}
\end{vmatrix}
$$

Double vertical bars

$$
\begin{Vmatrix}
x_{11} & x_{12} \\
x_{21} & x_{22}
\end{Vmatrix}
$$

Small

$$
\begin{smallmatrix}
x_{11} & x_{12} \\
x_{21} & x_{22}
\end{smallmatrix}
$$

Alignment

Cases

$$
f(x|\lambda) =
\begin{cases}
\lambda e^{-\lambda x} & x \geq 0, \\
0 & \text{otherwise}
\end{cases}
$$

Aligned

$$
\begin{aligned}
y_1 &= \beta_{11} + \beta_{12} x + \varepsilon_1 \\
y_2 &= \alpha_{21} y_1 + \beta_{21} + \beta_{22} x + \varepsilon_2
\end{aligned}
$$

Gathered

$$
\begin{gathered}
y_1 = \beta_{11} + \beta_{12} x + \varepsilon_1 \\
y_2 = \alpha_{21} y_1 + \beta_{21} + \beta_{22} x + \varepsilon_2
\end{gathered}
$$

Split

$$
\begin{split}
\mathop{E}\frac{\partial \ln L}{\partial \theta}
  &=\mathop{E}\left[\frac{1}{L} \frac{\partial L}{\partial \theta}\right]\\
  &=\int\left[\frac{1}{L} \frac{\partial L}{\partial \theta}\right] L\;dz\\
  &=\int\frac{\partial L}{\partial \theta}\;dz
\end{split}
$$