Patterns with several multiple eigenvalues

J. Dorsey; C.R. Johnson; Z. Wei

Special Matrices (2014)

  • Volume: 2, Issue: 1, page 200-205, electronic only
  • ISSN: 2300-7451

Abstract

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Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.

How to cite

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J. Dorsey, C.R. Johnson, and Z. Wei. "Patterns with several multiple eigenvalues." Special Matrices 2.1 (2014): 200-205, electronic only. <http://eudml.org/doc/269344>.

@article{J2014,
abstract = {Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.},
author = {J. Dorsey, C.R. Johnson, Z. Wei},
journal = {Special Matrices},
keywords = {multiple eigenvalues; patterned matrix; special periodic diagonal matrices (PDM); Symmetric Toeplitz matrices; special periodic diagonal matrices; symmetric Toeplitz matrices},
language = {eng},
number = {1},
pages = {200-205, electronic only},
title = {Patterns with several multiple eigenvalues},
url = {http://eudml.org/doc/269344},
volume = {2},
year = {2014},
}

TY - JOUR
AU - J. Dorsey
AU - C.R. Johnson
AU - Z. Wei
TI - Patterns with several multiple eigenvalues
JO - Special Matrices
PY - 2014
VL - 2
IS - 1
SP - 200
EP - 205, electronic only
AB - Identified are certain special periodic diagonal matrices that have a predictable number of paired eigenvalues. Since certain symmetric Toeplitz matrices are special cases, those that have several multiple 5 eigenvalues are also investigated further. This work generalizes earlier work on response matrices from circularly symmetric models.
LA - eng
KW - multiple eigenvalues; patterned matrix; special periodic diagonal matrices (PDM); Symmetric Toeplitz matrices; special periodic diagonal matrices; symmetric Toeplitz matrices
UR - http://eudml.org/doc/269344
ER -

References

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  1. [1] M. Farber, C.R. Johnson, Z. Wei, Eigenvalue pairing in the response matrix for a class of network models with circular symmetry, The Electronic Journal of Combinatorics, 20(3) (2013) paper 17 Zbl1295.05143
  2. [2] C.R. Johnson and A. Leal-Duarte, The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree. Linear and Multilinear Algebra 46:139-144 (1999) [WoS] Zbl0929.15005
  3. [3] C.R. Johnson and A. Leal-Duarte, On the possible multiplicities of the eigenvalues of an Hermitian matrix whose graph is a given tree. Linear Algebra and Its Applications 348:7-21 (2002) [WoS] Zbl1001.15004
  4. [4] C.R. Johnson, A. Leal-Duarte and C.M. Saiago, The parter-Wiener theorem: refinement and generalization. SIAM Journal on Matrix Analysis and Applications 25(2):352-361 (2003) [Crossref] Zbl1067.15003
  5. [5] C.R. Johnson, A. Leal-Duarte and C.M. Saiago, Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars. Linear Algebra and Its Applications 373:311-330 (2003) [WoS] Zbl1035.15010
  6. [6] C.R. Johnson, A. Leal-Duarte, C.M. Saiago andDSher, Eigenvalues, multiplicities and graphs. In Algebra and its Applications, D.V.Huynh, S.K. Jain, and S.R. López-Permouth, eds., Contemporary Mathematics, AMS, 419:17-1183 (2006) 
  7. [7] P. Lax, The multiplicity of eigenvalues. Journal of the American Mathematical Society 6:213-214 (1982) Zbl0483.15006
  8. [8] B. Türen, The eigenvalues of symmetric toeplitz matrices. Erciyes Üniversitesi Fen Bilimleri Dergisi 12(1-2):37-49 (1996) 

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