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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 <>,
comtech <> 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
>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

On the other hand, the singular values are unchanged.

Robert Israel
Department of Mathematics
University of British Columbia Vancouver, BC, Canada

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