DocumentCode
840201
Title
An algorithm to determine if two matrices have common eigenvalues
Author
Datta, Karabi
Author_Institution
Northern Illinois University, DeKalb, IL, USA
Volume
27
Issue
5
fYear
1982
fDate
10/1/1982 12:00:00 AM
Firstpage
1131
Lastpage
1133
Abstract
Given two real lower Hessenberg matrices 
and 
of order 
and 
, respectively, a symmetric matrix of order is constructed such that whenever 
is nonsingular, and do not have an eigenvalue in common. When is singular, its nullity, is the same as the number of common eigenvalues between and . A well-known classical result on the relative primeness of two polynomials and the associated Bezoutian matrix is included as a special case.
and of order and , respectively, a symmetric matrix of order is constructed such that whenever is nonsingular, and do not have an eigenvalue in common. When is singular, its nullity, is the same as the number of common eigenvalues between and . A well-known classical result on the relative primeness of two polynomials and the associated Bezoutian matrix is included as a special case.Keywords
Eigenvalues/eigenvectors; Matrices; Eigenvalues and eigenfunctions; Equations; Matrix decomposition; Polynomials; Symmetric matrices;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.1982.1103083
Filename
1103083
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