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? e-vectors of sum of rank one matrices
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Cheng Cosine
science forum Guru Wannabe


Joined: 26 May 2005
Posts: 168

PostPosted: Sat Jun 03, 2006 6:36 am    Post subject: ? e-vectors of sum of rank one matrices Reply with quote

Hi:

Given a vector a, the matrix A = a*a' is of rank one. Now suppose one has

a set of N-vector a_1, a_2, ..., a_M, where a_i is n-dim 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
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Roger Lui
science forum beginner


Joined: 07 Jul 2006
Posts: 1

PostPosted: Fri Jul 07, 2006 3:05 pm    Post subject: Re: ? e-vectors of sum of rank one matrices Reply with quote

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
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