# Determinant

## Determinant(c, I, J)

Computes the determinant of a square matrix, «c». Indexes «`I`

» and «`J`

» must be the same length, so that the matrix is square.

The determinant of a matrix is a useful value that is used heavily in linear algebra and matrix applications. The inverse of a matrix exists and is unique if and only if the determinant is non-zero.

Geometrically, the determinant can be viewed as the N-dimensional volume of the N-dimensional parallelepiped formed from the vectors in matrix «c». A parallelepiped in the N-dimensional generalization of a parallelogram (a 2-D parallelepiped is a parallelogram). Each vertex of the parallelepiped is obtained by taking a subset of the slices along «`J`

» and adding them together. The empty subset is the origin. There are `2^N`

subsets, where `N=Size(J)`

.

## Examples

The determinant of the identity matrix is 1.

`Determinant(I=J,I,J) → 1`

`Determinant(c,I,J)`

→ 15

`Determinant(c,I,J)`

→ -114 - 68j

`Variable Matrix :=`

M ▶ L ▼ 1 2 3 4 5 1 6 2 6 3 1 2 2 4 3 1 3 3 6 3 9 3 4 4 3 1 3 8 4 5 1 3 4 4 7

`Determinant(Matrix,L,M) → 359`

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