The DET function computes the determinant of a square matrix. The determinant, the product of the eigenvalues, is a scalar numeric value. If the determinant of a matrix is zero, then the matrix is singular. A singular matrix does not have an inverse.

The DET function performs an LU decomposition and collects the product of the diagonals (Forsythe, Malcom, and Moler, 1967). For a matrix with rows, the DET function allocates a temporary array in order to compute the determinant.

The following statements compute the determinant of a matrix:

a = {1 1 1,
     1 2 4,
     1 3 9};
d = det(a);
print d;

The DET function uses a criterion to determine whether the input matrix is singular. See the INV function for details.