Math Programming: Determining Determinants

Here is a version John Clark presented to his students in 1983 to illustrate recursive functions:

If an n x n matrix is upper triangular, then det(A) = a₁₁a₂₂...a_nn¹. This version uses row reduction to get the input matrix [m] in upper triangular form and computes the determinant from the diagonal product.

Here's an example, given matrix "A":

0.54 0.26 0.42 1.52 0.16 0.92 1.94 0.48
0.4  1.38 0.18 1.72 0.32 0.26 1.62 1.9
0.1  0.14 1.66 0.3  1.62 0.46 0.8  1.2
1.32 0.12 1.98 1.64 0.84 0.08 0.22 1.96
1.74 1.36 1.68 0.48 1.44 1.18 0.46 0.46
0.02 0.9  0.82 1.88 0.06 1.04 0.76 1.72
1.6  1.22 0.68 1.26 1.32 1.3  0.52 0.06
1.98 0.42 1.3  1.14 0.76 0.26 0.9  0.28

Find the determinant from the APL prompt type:

   det A

Result: -10.3

1.  O'neil, Peter, Advanced Engineering Mathematics, 4th ed., 1995, Theorem 8.26, p387