An atlas for tridiagonal isospectral manifolds

Details An atlas for tridiagonal isospectral manifolds An atlas for tridiagonal isospectral manifolds

2006-08-22

arxiv.org/abs/math/0608558v5

Linear Algebra and its Applications 429 (2008) 387-402

Mathematics

Spectral Theory

Fixed typos; 16 pages, 3 figures

Scientific paper

10.1016/j.laa.2008.03.001

Let ${\cal T}_\Lambda$ be the compact manifold of real symmetric tridiagonal matrices conjugate to a given diagonal matrix $\Lambda$ with simple spectrum. We introduce {\it bidiagonal coordinates}, charts defined on open dense domains forming an explicit atlas for ${\cal T}_\Lambda$. In contrast to the standard inverse variables, consisting of eigenvalues and norming constants, every matrix in ${\cal T}_\Lambda$ 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.

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