Date: Feb 22, 2013 11:56 AM
Author: fl
Subject: Re: Question about null basis of a matrix A (linear algebra)
On Friday, February 22, 2013 11:53:55 AM UTC-5, rxj...@gmail.com wrote:

> Hi,

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

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> The hand-out first talked think matrix V(rXr) in SVD: A V=U Sigma

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> Later it introduced full matrix V. V was not seen to increase dimension from r to n in either row or column.

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

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> Thanks,

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> .............

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> range and null space

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> if r = rank(A), then

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> ? {u1, . . . , ur} are an orthonormal basis for range(A)

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> ? {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.