Patterns with several multiple eigenvalues

• Autorzy: J. Dorsey , C.R. Johnson , Z. Wei
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

multiple eigenvalues; patterned matrix; special periodic diagonal matrices (PDM); Symmetric Toeplitz matrices

Kategorie tematyczne

• 15B99: None of the above, but in this section
• 15A18: Eigenvalues, singular values, and eigenvectors
• 15B57: Hermitian, skew-Hermitian, and related matrices
• 15B05: Toeplitz, Cauchy, and related matrices

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-07-28

zaakceptowano

2014-12-02

online

2014-12-09

Twórcy

autor

J. Dorsey

• Department of Mathematics, Imperial College London, UK

autor

C.R. Johnson

• Department of Mathematics, Case Western Reserve University, Ohio, USA

autor

Z. Wei

• Department of Mathematics, College of William and Mary, Virginia, USA

Bibliografia

• [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
• [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]
• [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]
• [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]
• [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]
• [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)
• [8] B. Türen, The eigenvalues of symmetric toeplitz matrices. Erciyes Üniversitesi Fen Bilimleri Dergisi 12(1-2):37-49 (1996)

Identyfikatory

DOI

10.2478/spma-2014-0020