Language Reference

DET Function

DET (square-matrix);

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 n rows, the DET function allocates a temporary $n^2$ 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;

Figure 24.101: Determinant of a Matrix

d
2 




            

            


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