karl
Posts:
398
Registered:
8/11/06


Re: Does this matrix function have real eigenvalues?
Posted:
Jul 28, 2012 12:24 AM


Am 28.07.2012 04:21, schrieb Paul: > Let G = I  inv(W) * B where W and B are real symmetric positive > definite matrices. > In simulations it appears that G always has real eigenvalues, though G > is not necessarily symmetric or positive definite. > > I wonder if it can be proved in general that G has real eigenvalues? > Bonus question: Is there a simple relationship between the eigenvalues > of G and those of W and B? > > Best, > Paul >
G= inv(W)*(WB)= inv(W)*Winv(W)*B=Iinv(W)*B. Inv(W) and WB are symmetric, therefore their product will be symmetric too AFAIS.
Karl

