On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph
For Hermitian matrices, whose graph is a given tree, the relationships among vertex degrees, multiple eigenvalues and the relative position of the underlying eigenvalue in the ordered spectrum are discussed in detail. In the process, certain aspects of special vertices, whose removal results in an i...
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| Published in | Linear algebra and its applications Vol. 363; pp. 147 - 159 |
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| Main Authors | , , , , |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
New York, NY
Elsevier Inc
01.04.2003
Elsevier Science |
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| Abstract | For Hermitian matrices, whose graph is a given tree, the relationships among vertex degrees, multiple eigenvalues and the relative position of the underlying eigenvalue in the ordered spectrum are discussed in detail. In the process, certain aspects of special vertices, whose removal results in an increase in multiplicity are investigated. |
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| AbstractList | For Hermitian matrices, whose graph is a given tree, the relationships among vertex degrees, multiple eigenvalues and the relative position of the underlying eigenvalue in the ordered spectrum are discussed in detail. In the process, certain aspects of special vertices, whose removal results in an increase in multiplicity are investigated. |
| Author | Saiago, Carlos M. Sutton, Brian D. Leal Duarte, António Witt, Andrew J. Johnson, Charles R. |
| Author_xml | – sequence: 1 givenname: Charles R. surname: Johnson fullname: Johnson, Charles R. organization: Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA – sequence: 2 givenname: António surname: Leal Duarte fullname: Leal Duarte, António organization: Dep. de Matemática, Univ. de Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal – sequence: 3 givenname: Carlos M. surname: Saiago fullname: Saiago, Carlos M. organization: Dep. de Matemática, Fac. de Ciências e Tecnologia da Univ. Nova de Lisboa, 2829-516 Monte Caparica, Portugal – sequence: 4 givenname: Brian D. surname: Sutton fullname: Sutton, Brian D. email: bsutton@math.mit.edu organization: Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0123, USA – sequence: 5 givenname: Andrew J. surname: Witt fullname: Witt, Andrew J. organization: Department of Mathematics, Brigham Young University, Provo, UT 84602, USA |
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| Cites_doi | 10.1080/03081089908818608 10.1137/0108024 10.1016/0024-3795(84)90019-3 |
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| Keywords | Eigenvalues Hermitian matrix Vertex degress Tree Parter vertices Multiplicity |
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| References | Wiener (BIB4) 1984; 61 Horn, Johnson (BIB1) 1985 Parter (BIB3) 1960; 8 Johnson, Leal Durate (BIB2) 1999; 46 Johnson (10.1016/S0024-3795(01)00589-4_BIB2) 1999; 46 Horn (10.1016/S0024-3795(01)00589-4_BIB1) 1985 Parter (10.1016/S0024-3795(01)00589-4_BIB3) 1960; 8 Wiener (10.1016/S0024-3795(01)00589-4_BIB4) 1984; 61 |
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| SubjectTerms | Algebra Eigenvalues Exact sciences and technology Hermitian matrix Linear and multilinear algebra, matrix theory Mathematics Multiplicity Parter vertices Sciences and techniques of general use Tree Vertex degress |
| Title | On the relative position of multiple eigenvalues in the spectrum of an Hermitian matrix with a given graph |
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