Cheng Cosine science forum Guru Wannabe
Joined: 26 May 2005
Posts: 168

Posted: Sat Jun 03, 2006 6:36 am Post subject:
? evectors of sum of rank one matrices



Hi:
Given a vector a, the matrix A = a*a' is of rank one. Now suppose one has
a set of Nvector a_1, a_2, ..., a_M, where a_i is ndim unit column vector.
A matrix
B is defined as: B = c1*a_1*a_1'+c2*a_2*a_2'+...+cM*a_M*a_M', M >= N, c's
are
scalars. Are there relations between eigenvectors of B to the given set of
vectors a_m?
Thanks,
by Cheng Cosine
Jun/03/2k6 NC 

Roger Lui science forum beginner
Joined: 07 Jul 2006
Posts: 1

Posted: Fri Jul 07, 2006 3:05 pm Post subject:
Re: ? evectors of sum of rank one matrices



Hi,
I came across that problem as well but M < N and all I need to know is the rank of B. I think if a_i's are independent, then rank of B is M but I don't have a proof of that. Do you know?
Roger 
