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.
@article{bwmeta1.element.doi-10_2478_spma-2014-0020, author = {J. Dorsey and C.R. Johnson and Z. Wei}, title = {Patterns with several multiple eigenvalues}, journal = {Special Matrices}, volume = {2}, year = {2014}, zbl = {1310.15052}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0020} }
J. Dorsey; C.R. Johnson; Z. Wei. Patterns with several multiple eigenvalues. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0020/
[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 | Zbl 1295.05143
[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] | Zbl 0929.15005
[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] | Zbl 1001.15004
[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] | Zbl 1067.15003
[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] | Zbl 1035.15010
[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] P. Lax, The multiplicity of eigenvalues. Journal of the American Mathematical Society 6:213-214 (1982) | Zbl 0483.15006
[8] B. Türen, The eigenvalues of symmetric toeplitz matrices. Erciyes Üniversitesi Fen Bilimleri Dergisi 12(1-2):37-49 (1996)