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Topic:
Question about null basis of a matrix A (linear algebra)
Replies:
2
Last Post:
Feb 24, 2013 12:09 PM



fl
Posts:
121
Registered:
10/8/05


Re: Question about null basis of a matrix A (linear algebra)
Posted:
Feb 22, 2013 11:56 AM


On Friday, February 22, 2013 11:53:55 AM UTC5, rxj...@gmail.com wrote: > Hi, > > > > I read a handout from a website on SVD. I do not understand the last line below dot line. > > > > The handout 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? > > Thanks, > > > > ............. > > 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)
It did increase V from rXr to rXn. I have to find how it increases the columns. Thanks.



