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Bidiagonal factorizations with some parameters equal to zero

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 2011 English Publisher:Elsevier BVJournal:Linear Algebra and its Applications, volume 434, pages 730-740 (issn: 0024-3795, Copyright policy )
Authors: Huang, Rong; Liu, Jianzhou;

doi: 10.1016/j.laa.2010.09.033

Bidiagonal factorizations with some parameters equal to zero

Abstract

This paper deals with the bidiagonal factorization of complex matrices. By the means of the new concepts of relevant submatrix and almost totally nonsingular matrix, necessary and sufficient conditions are obtained for a nonsingular matrix to have a bidiagonal factorization with some parameters of the subdiagonal (or superdiagonal) being equal to zero. Some additional results for almost totally nonsingular matrices are presented.

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Keywords

Numerical Analysis, Eigenvalues, singular values, and eigenvectors, complex matrices, Algebra and Number Theory, relevant submatrix, Inequalities involving eigenvalues and eigenvectors, Factorization of matrices, bidiagonal factorization, Totally nonsingular matrices, almost totally nonsingular matrix, Discrete Mathematics and Combinatorics, Bidiagonal factorization, Geometry and Topology

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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