Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 132-149
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V. N. Kublanovskaya. To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 132-149. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a9/
@article{ZNSL_2005_323_a9,
author = {V. N. Kublanovskaya},
title = {To solving multiparameter problems of algebra.~6. {Spectral} characteristics of polynomial matrices},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {132--149},
year = {2005},
volume = {323},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a9/}
}
TY - JOUR
AU - V. N. Kublanovskaya
TI - To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2005
SP - 132
EP - 149
VL - 323
UR - http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a9/
LA - ru
ID - ZNSL_2005_323_a9
ER -
%0 Journal Article
%A V. N. Kublanovskaya
%T To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 132-149
%V 323
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a9/
%G ru
%F ZNSL_2005_323_a9
For a $q$-parameter polynomial $m\times n$ matrix $F$ of rank $\rho$, solutions of the equation $Fx=0$ at points of the spectrum of the matrix $F$ determined by the $(q-1)$-dimensional solutions of the system $Z[F]=0$ are considered. Here, $Z[F]$ is the polynomial vector whose components are all possible minors of order $\rho$ of the matrix $F$. A classification of spectral pairs in terms of the matrix $A[F]$, with which the vector $Z[F]$ is associated, is suggested. For matrices $F$ of full rank, a classification and properties of spectral pairs in terms of the so-called levels of heredity of points of the spectrum of $F$ are also presented.
