ABSTRACT
Diagonal matrices are about the nicest matrices around. It is easy to add, subtract, and multiply them; find their inverses (if they happen to be invertible); and find their pseudoinverses. The question naturally arises, is it possible to express an arbitrary matrix in terms of diagonal ones? Let’s illustrate just how
easy this is to do. Consider A =
1 1 2 1 2 2 1 1 2 1 2 2
. Note A is 4-by-3 with rank 2.
First, write A in a full rank factorization; A =
