For a matrix, for instance, like:

\begin{equation} \begin{bmatrix} a & b \\ c & d \end{bmatrix} \end{equation}

We wish to find the matrix’s determinant; we write it down as:

\begin{equation} \begin{vmatrix} a & b \\ c & d \end{vmatrix} \end{equation}

## geometric interpretation of determinants

Geometrically, determinants are how matrices send a unit object after its mapping; i.e. how does it transform the area of a unit square.

## determinants can be computed along any axes

You can pick any row or column as the “axes”, and expand the matrix along any direction