Start with a diagonal matrix (not necessarily square) and use `rcop' to generate an equivalent matrix (recall that the output of any rcop is equivalent to the input) that is not at all diagonal, the more complicated the better. (For an easy method of entering diagonal matrices, see Generating examples using Matlab functions.) Then apply `quick' to find an equivalent diagonal matrix. Note that, if, for example, you start with the 2x2 diagonal matrix whose diagonal entries are 2, 1, the equivalent diagonal matrix you end up with may not be the same. In other words, equivalent diagonal matrices need not be equal.
On the other hand, the outcome of the proposed experiment, even if it is not the original diagonal matrix, will always resemble it in certain respects. See if you can discover any rules that relate equivalent diagonal matrices. This is a topic worthy of lots of experiments. Notice that there is a marked difference between square matrices and matrices that are not square when it comes to the matter of the signs of the entries of equivalent diagonal matrices. (Chapter 5 gives a complete solution of the problem of determining whether two diagonal matrices are equivalent.)
Return to Chapter 2.