det

Determinant of a square matrix.

Category: Mathematics > Linear Algebra

Syntax

d = det(A)

Description

det factors the matrix with lu and multiplies the diagonal of U by the sign of the permutation. The result is exact for small integer matrices only up to rounding, so a singular matrix can return a tiny nonzero value instead of 0.

The determinant is a poor test for singularity, because it scales with the entries: multiplying an n-by-n matrix by 10 multiplies the determinant by 10^n. Use rank or cond instead.

Input arguments

A

Square matrix.

Output arguments

d

Scalar determinant. The determinant of an empty matrix is 1.

Example

Small matrices

det([1 2; 3 4])
det(magic(3))
det(eye(3))
det([])

ans = -2
ans = -360
ans = 1
ans = 1

See also

inv lu rank cond trace