svd question

ds · science forum beginner Joined: 22 Jun 2006 Posts: 1

Hi all,

I hope this is the right place to ask and sorry for cross-posting. I am
facing the following
problem:

1) vector ai belongs to some R^n subspace W.
2) matrix A=[a1 a2 a3 ... an]^T is a mxn matrix of vectors
3) A=USV^T according to the SVD where V is a nxn matrix of
eigenvectors.

now, the singular vectors vi, do they belong to W? Or, in other words,
what are the conditions that this proposition holds? For example one
might write:

vi=(1/si)*A^T*ui. Therefore, if W=span(ai)then the proposition will
hold. But let's say D is a real positive definite and symmetric matrix
with eigenvalues E and W=ran(E) and ai belong to W. But also span(ai)
belongs to ran(E). As a conclusion, if all this holds then the right
singular vectors are linear combinations of the eigenvectors if all of
the above hold. Does anyone like any of this or am I a complete idiot?
Any help will be greatly appreciated.

TIA and cheers

dps

Peter Spellucci · science forum Guru Joined: 29 Apr 2005 Posts: 702

In article <e7dvnm$gpn$1@dizzy.math.ohio-state.edu>,
"ds" <junkmailavoid@yahoo.com> writes:

ds · science forum beginner Joined: 23 Jun 2006 Posts: 1

Hello Peter,

Google