We derive the interlacing properties of the eigenvalues of a symmetric matrix with those of its largest principal submatrix using root-locus ideas. We then give a sufficient condition for distinctness of eigenvalues based on the minimality of an associated linear system.
%0 Journal Article
%1 dickinson80
%A Dickinson, B.W.
%A Steiglitz, K.
%D 1980
%J Automatic Control, IEEE Transactions on
%K eigenvalues linear.algebra matrix
%N 2
%P 284--285
%R 10.1109/TAC.1980.1102293
%T Eigenvalues of Symmetric Matrices: System Theory Conditions for Distinctness
%V 25
%X We derive the interlacing properties of the eigenvalues of a symmetric matrix with those of its largest principal submatrix using root-locus ideas. We then give a sufficient condition for distinctness of eigenvalues based on the minimality of an associated linear system.
@article{dickinson80,
abstract = {We derive the interlacing properties of the eigenvalues of a symmetric matrix with those of its largest principal submatrix using root-locus ideas. We then give a sufficient condition for distinctness of eigenvalues based on the minimality of an associated linear system.},
added-at = {2015-09-17T10:37:54.000+0200},
author = {Dickinson, B.W. and Steiglitz, K.},
biburl = {https://www.bibsonomy.org/bibtex/2e9b803d9f642934dd44ea24c56349f38/ytyoun},
doi = {10.1109/TAC.1980.1102293},
interhash = {b804300b31e8c13a49579fcdeaa0cd06},
intrahash = {e9b803d9f642934dd44ea24c56349f38},
issn = {0018-9286},
journal = {Automatic Control, IEEE Transactions on},
keywords = {eigenvalues linear.algebra matrix},
month = apr,
number = 2,
pages = {284--285},
timestamp = {2016-06-12T12:58:53.000+0200},
title = {Eigenvalues of Symmetric Matrices: System Theory Conditions for Distinctness},
volume = 25,
year = 1980
}