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
Link To Document :
