# Math#

## Notation#

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

```
$$
\begin{aligned}
\end{aligned}
$$
```

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

```
$$
x_y = 2
$$ (label)
```

which can be referenced using the role

```
and here is the reference to {eq}`label`
```