# Math
## Notation
```{margin}
Example notation can be found [here](https://python.quantecon.org/lqcontrol.html)
```
Use `\top`(e.g., $A^\top$) to represent the transpose of a vector or matrix.
Use `\mathbb{1}`($\mathbb{1}$) to represent a vector or matrix of ones and explain it in the lecture (e.g., "Let $\mathbb{1}$ be an $n \times 1$ vector of ones...").
Matrices always use square brackets and `\begin{bmatrix} ... \end{bmatrix}` should be used.
Do **not** use `bold face` for either matrices or vectors
Sequences use curly brackets, such as `\{ x_t \}_{t=0}^{\infty}`
The use of align environments can be done using the `\begin{aligned} ... \end{aligned}`
when inside a math environment such as `$$`
:::{tip}
**PDF:**
Using `aligned` when inside a math environment (such as `$$`) is important
for building `pdf` output
```md
$$
\begin{aligned}
\end{aligned}
$$
```
This is because the `$$` is already a math environment and causes the LaTeX build
to fail when using `align` due to the issue of multiple math environments.
The LaTeX `aligned` environment is purpose built for using within `math` environments.
:::
It is also important to **not** use `\tag` in equations for manual equation numbering and instead
make use of the in-built equation numbering such as
```md
$$
x_y = 2
$$ (label)
```
which can be referenced using the role
```md
and here is the reference to {eq}`label`
```