Date: Feb 22, 2013 11:53 AM
Author: fl
Subject: Question about null basis of a matrix A (linear algebra)


I read a hand-out from a website on SVD. I do not understand the last line below dot line.

The hand-out first talked think matrix V(rXr) in SVD: A V=U Sigma
Later it introduced full matrix V. V was not seen to increase dimension from r to n in either row or column.

But below it talked about r+1....n. How to understand this differences?

range and null space
if r = rank(A), then
? {u1, . . . , ur} are an orthonormal basis for range(A)
? {vr+1, . . . , vn} are an orthonormal basis for null(A)