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Linear Algebra and its Applications
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Linear Algebra and its Applications
Article . 1993
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Linear Algebra and its Applications
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A matrix pair of an almost diagonal skew-symmetric matrix and a symmetric positive definite matrix

Authors: Vjeran Hari; Noah H. Rhee;

A matrix pair of an almost diagonal skew-symmetric matrix and a symmetric positive definite matrix

Abstract

Let A be skew-symmetric, B be symmetric positive definite, and the pair (A, B) have multiple eigenvalues. If A is close to Murnaghan form and B is close to diagonal form, then certain principal submatrices of A and B are specially related. In this paper we describe this relationship and quantify it under the usual asymptotic conditions. If B=I, the identity matrix, the result describes a special structure of a skew-symmetric matrix almost in Murnaghan form. We then briefly discuss how the Paardekooper method for skew-symmetric matrices asymptotically behaves in the presence of multiple eigenvalues.

Country
Croatia
Keywords

Numerical computation of eigenvalues and eigenvectors of matrices, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, skew-symmetric, symmetric positive definite, asymptotic behavior of diagonalization methods, Murnaghan form, quadratic convergence, generalized skew-symmetric eigenvalues problem, Paardekooper method, almost diagonal matrix pair, Discrete Mathematics and Combinatorics, Hermitian, skew-Hermitian, and related matrices, multiple eigenvalues, Geometry and Topology, Almost diagonal matrices; pair of a skew-symmetric and a positive definite matrix

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citations
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!
2
Average
Average
Average
hybrid