[R] SVD least squares sub-space projection
José Augusto M. de Andrade Junior
jamaj69 at gmail.com
Sun Jan 6 01:35:04 CET 2008
Hi all,
A good new year for everybody.
Could somebody help me on a question?
The Singular Value Decomposition of a matrix A gives A = U * D * t(V)
I A is a M X N matrix, U is the left singular matrix (M X N), D is a
diagonal singular values matrix (N X N) and V is the transpose right
singular ortogonal matrix (N X N).
By taking the first l columns of V, with gives a (l X l) matrix, i
know that i than have a sub-space (R^L)of the original (R^M) space. I
know that this sub-space basis is optimal in the least squares sense.
The question is: given one 3-dim space generated by 6 vectors (A is a
6X3 matrix), i define a 2-dim orthonormal basis by taking the 2 first
columns of V, how i can then project a new 3-dim vector in this 2-dim
sub-space just defined?
Thanks in advance.
José Augusto M. de Andrade Jr.
Business Adm. Student
University of Sao Paulo - Brazil
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