The canonical structure of a pencil of degenerate matrix functions
type: Item
instance of: scholarly article
title: The canonical structure of a pencil of degenerate matrix functions
zbMATH Open document ID: 1257.15008
DOI: 10.3103/S1066369X1202003X
author: S. V. Gaidomak
published in: Russian Mathematics
publication date: 2012-11-20T00:00:00Z
review text: The author studies global properties of a pencil of identically degenerate matrix functions with a compact domain of definition. The matrix functions are assumed to have a constant rank and all roots of the characteristic equation of the matrix pencil are assumed to have a constant multiplicity at each point in the domain of definition. He obtains sufficient conditions for the smooth orthogonal similarity of the matrix functions to the upper triangular form and sufficient conditions for the smooth equivalence of the pencil of matrix functions to its canonical form. He also illustrates the obtained results with simple examples.
reviewed by: Andreas Arvanitoyeorgos
Mathematics Subject Classification ID: 15A22
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15A54
zbMATH DE Number: 6108779
zbMATH Keywords: matrix functions
zbMATH Keywords: pencils
zbMATH Keywords: canonical structure
zbMATH Keywords: \(p\)-smoothly similar matrix functions
zbMATH Keywords: \(p\)-smoothly equivalent matrix pencils
zbMATH Keywords: degenerate matrix functions
zbMATH Keywords: constant rank
zbMATH Keywords: orthogonal similarity
zbMATH Keywords: canonical form
MaRDI profile type: Publication
cites work: Q5640694
cites work: Three-layer finite-difference method for linear partial differential-algebraic systems
cites work: Stability of an implicit difference scheme for a linear differential-algebraic system of partial differential equations
cites work: Q3254327
cites work: The existence of a continuous basis of a certain linear subspace of $E\sb{r}$ which depends on a parameter
cites work: Generalizations of a theorem of doležal
cites work: Globally analytic triangularization of a matrix function
cites work: A global analysis of matrices of functions of several variables
description: scientific article; zbMATH DE number 6108779