ABSTRACT
It is inconvenient to pursue this further for general matrices. InsteacL we can derive more insight by considering the case where we have chosen the basis vectors for x to be the eigenvectors of AtA, so that AtA is diagonal; i.e., we use the canonical form introduced in §5.11, where I showed that any matrix equation can, by a proper choice of basis vectors, be expressed in the form
where D is a diagonal matrix, the components of x vary independently, and so do the components of y. I can also write this relationship yi=? ixi. Also, remember that the singular values ?i=0 for all i .
