GNU Octave

Time for action – using Octave for advanced linear algebra

1. It is easy to calculate the determinant of a 2 x 2 matrix, but for a 3 x 3 matrix, the calculation becomes tedious, not to mention larger size matrices. Octave has a function det that can do this for you:

   octave:46> A=[2 1 -3; 4 -2 -2; -1 0.5 -0.5];
   
   octave:47>det(A)
   
   ans = 8
   

   Recall from linear algebra that the determinant is only defined for a square n x n matrix. Octave will issue an error message if you pass a non-square matrix input argument.

2. Let us change A a bit:

   This result is consistent with the result from Chapter 2. A does not have full rank, that is, the determinant is 0.

   octave:48> A=[2 1 -3; 4 -2 -2; -2 1 1];
   
   octave:49>det(A)
   
   ans = 0
   

3. The eigenvalues of an n x n matrix are given ...