For example, when transforming a symmetric matrix with respect to a new basis, students can see that the use of an orthonormal basis will preserve symmetry. Using the package to introduce or extend techniques and concepts is more motivating. For example, in moving from the power method with a diagonal form matrix to the inverse power method, students are asked to enter a short Matlab program which will carry out the procedure. This helps them to think about what is happening rather than just accepting the Matlab results. For example, special patterned matrices can be investigated to see whether their pattern is preserved after inversion.
Students become familiar with the use of a real package in practice.
For example, they can look at what happens to matrices without a full set of eigenvectors. The use of computers has some disadvantages too. Some students will try and use Matlab on every problem, when in fact the aim is that they should think about the problem first, and only use a package if that is appropriate. It is also necessary to warn students that they need to choose an appropriate technique, and tutors that some topics which can take advantage of Matlab may well be too advanced in concept for students. For example, Matlab will carry out the Cholesky decomposition for non-symmetric matrices giving an upper triangular matrix with no comment.