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Topic: eigenvalues and row transformations?
Replies: 3   Last Post: May 23, 2006 1:39 PM

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Robert Israel

Posts: 11,902
Registered: 12/6/04
Re: eigenvalues and row transformations?
Posted: May 23, 2006 1:39 PM
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In article <1148335764.271492.302400@y43g2000cwc.googlegroups.com>,
comtech <comtech.usa@gmail.com> wrote:

>If I have a matrix, and I apply elementary row operations on it. For
>example, I apply a row-changing matrix to multiply to the original
>matrix from the left hand-side, so I exchange two rows in the original
>matrix.
>
>How does this operation affect the eigenvalues?


As has been mentioned, the row swap will multiply the determinant (which
is the product of the eigenvalues, counting multiplicities) by -1.
Otherwise there's not very much to be said about the effect on the
eigenvalues.

On the other hand, the singular values are unchanged.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada




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