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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

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

Date Subject Author
2/22/13 fl
2/22/13 fl
2/24/13 J. Antonio Perez M.