[Numpy-discussion] Identifying Colinear Columns of a Matrix

[Charles R Harris]

On Fri, Aug 26, 2011 at 12:38 PM, Mark Janikas <mjanikas at esri.com> wrote:

> Charles!  That looks like it could be a winner!  It looks like you always
> choose the last column of the U matrix and ID the columns that have the same
> values?  It works when I add extra columns as well!  BTW, sorry for my lack
> of knowledge… but what was the point of the dot multiply at the end?  That
> they add up to essentially zero, indicating singularity?  Thanks so much!
>

The indicator of collinearity is the singular value in d, the corresponding
column in u represent the linear combination of rows that are ~0, the
corresponding row in v represents the linear combination of columns that are
~0. If you have several combinations that are ~0, of course you can add them
together and get another. Basically, if you take the rows in v corresponding
to small singular values, you get a basis for the for the null space of the
matrix, the corresponding columns in u are a basis for the orthogonal
complement of the range of the matrix. If that is getting a bit technical
you can just play around with things.

<snip>

Chuck
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