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Re: eigenvalues and row transformations?
Posted:
May 23, 2006 1:39 PM


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 rowchanging matrix to multiply to the original >matrix from the left handside, 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



