wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        general >> wanted >> Re: eigenvalues property ?
        
(Message started by: MonicaMath on Mar 28^th, 2009, 8:29pm)

Title: Re: eigenvalues property ?
Post by MonicaMath on Mar 28^th, 2009, 8:29pm

maybe you can start with:

since r is not an eigenvalue for A then det(r*I - A) not zero, so (A-r*I) is nonsingular, and use the fact that Bx=r*x, then show that
|| inv(r*I - A) (B-A) ||<1 to obtain a contradiction.

Title: Re: eigenvalues property ?
Post by trusure on Mar 28^th, 2009, 9:33pm

I tried your method but there is no result ?!

can anyone give me a hint ! ::)

Title: Re: eigenvalues property ?
Post by Eigenray on Mar 29^th, 2009, 5:31pm

Well that's a funny problem. Note that

(r I - A)^-1(B-A)
= (r I - A)^-1( (r I - A) + (B - r I) )
= I + C,
where C = (r I - A)^-1(B - r I) is a singular matrix. Do you know the following result: if || I + C || < 1, then C is non-singular?