res = det(x) returns the determinant of square matrix x.

Sparse double, single, complex double, and complex single matrices are supported. The result keeps single precision for single inputs.

For a

$$2 \times 2$$

matrix:

$$\det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc$$

For larger matrices, the determinant can be computed using cofactor expansion:

$$\det(A) = \sum_{j=1}^{n} (-1)^{i+j} a_{ij} M_{ij}$$

where

$$M_{ij}$$

is the minor of element

$$a_{ij}$$