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

With c → Determinant example1.png,

Determinant(c,I,J) → 15

With c → Determinant example2.png,

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

See Also

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