[Numpy-discussion] On the difference of two positive definite matrices

[denis]

Charles R Harris <charlesr.harris <at> gmail.com> writes:
 
> 
> On Sun, Dec 16, 2012 at 6:20 PM, Virgil Stokes <vs <at> it.uu.se> wrote:
> Suppose I have two positive definite matrices, A and B. Is it possible
> to use U*D*U^T  factorizations of these matrices to obtain a numerically
> stable result for their difference, A - B ?
...
 
> Not sure what you are asking, but there is a coordinate system in which they
> are both diagonal. Nevertheless, the difference may not be positive 
> definite.Chuck 

http://en.wikipedia.org/wiki/Positive-definite_matrix
#Simultaneous_diagonalization
shows how to do that, but
"note that this is no longer an orthogonal diagonalization";
orthogonal can do it iff A and B commute.
cheers
  -- denis