An atlas for tridiagonal isospectral manifolds

Let T Λ be the compact manifold of real symmetric tridiagonal matrices conjugate to a given diagonal matrix Λ with simple spectrum. We introduce bidiagonal coordinates, charts defined on open dense domains forming an explicit atlas for T Λ . In contrast to the standard inverse variables, consisting...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2008-07, Vol.429 (1), p.387-402
Main Authors: Leite, Ricardo S., Saldanha, Nicolau C., Tomei, Carlos
Format: Article
Language:English
Subjects:
Algebra
Exact sciences and technology
Jacobi matrices
Linear and multilinear algebra, matrix theory
Mathematics
Norming constants
QR algorithm
Sciences and techniques of general use
Toda flows
Tridiagonal matrices
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let T Λ be the compact manifold of real symmetric tridiagonal matrices conjugate to a given diagonal matrix Λ with simple spectrum. We introduce bidiagonal coordinates, charts defined on open dense domains forming an explicit atlas for T Λ . In contrast to the standard inverse variables, consisting of eigenvalues and norming constants, every matrix in T Λ now lies in the interior of some chart domain. We provide examples of the convenience of these new coordinates for the study of asymptotics of isospectral dynamics, both for continuous and discrete time.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2008.03.001