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2 results on '"Hermitian matrix"'

1. THE PARTER --WIENER THEOREM:REFINEMENT AND GENERALIZATION.

Author

Johnson, Charles R., Duarte, António Leal, and Saiago, Carlos M.

Subjects
*EIGENVALUES, *HERMITIAN forms, *MULTIPLICITY (Mathematics), *MATRICES (Mathematics), *VERTEX operator algebras, *GENERALIZED integrals
Abstract

An important theorem about the existence of principal submatrices of a Hermitian matrix whose graph is a tree, in which the multiplicity of an eigenvalue increases, was largely developed in separate papers by Parter and Wiener. Here, the prior work is fully stated, then generalized with a self-contained proof. The more complete result is then used to better understand the eigenvalue possibilities of reducible principal submatrices of Hermitian tridiagonal matrices. Sets of vertices, for which the multiplicity increases, are also studied. [ABSTRACT FROM AUTHOR]

Published
2003
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2. The Parter-Wiener theorem: Refinement and generalization

Author

António Leal Duarte, Carlos M. Saiago, Charles R. Johnson, CMA - Centro de Matemática e Aplicações, and DM - Departamento de Matemática

Subjects
Tridiagonal matrix, Block matrix, Multiplicity (mathematics), Eigenvalues, Vertex degrees, Hermitian matrix, Parter vertices, Graph, Combinatorics, Multiplicity, Analysis, Eigenvalues and eigenvectors, Tree, Mathematics
Abstract

An important theorem about the existence of principal submatrices of a Hermitian matrixwhose graph is a tree, in which the multiplicity of an eigenvalue increases, was largely developed in separate papers by Parter and Wiener. Here, the prior work is fully stated, then generalized with a self-contained proof. The more complete result is then used to better understand the eigenvalue possibilities of reducible principal submatrices of Hermitian tridiagonal matrices. Sets of vertices, for which the multiplicity increases, are also studied. publishersversion published

Published
2004

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