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)*(W-B)= inv(W)*W-inv(W)*B=I-inv(W)*B. Inv(W) and W-B are symmetric, therefore their product will be symmetric too AFAIS.