Campus Units
Mathematics
Document Type
Article
Publication Version
Submitted Manuscript
Publication Date
10-2006
Journal or Book Title
Linear Algebra and its Applications
Volume
418
DOI
10.1016/j.laa.2006.02.017
Abstract
A sign pattern is a matrix whose entries are elements of {+, −, 0}; it describes the set of real matrices whose entries have the signs in the pattern. A graph (that allows loops but not multiple edges) describes the set of symmetric matrices having a zero-nonzero pattern of entries determined by the absence or presence of edges in the graph. DeAlba et al. [L.M. DeAlba, T.L. Hardy, I.R. Hentzel, L. Hogben, A. Wangsness, Minimum rank and maximum eigenvalue multiplicity of symmetric tree sign patterns, Linear Algebra Appl., in press, doi:10.1016/j.laa.2006.02.018.] gave algorithms for the computation of maximum multiplicity and minimum rank of matrices associated with a tree sign pattern or tree, and an algorithm to obtain an integer matrix realizing minimum rank. We extend these results by giving algorithms to obtain a symmetric rational matrix realizing the maximum multiplicity of a rational eigenvalue among symmetric matrices associated with a symmetric tree sign pattern or tree.
Rights
This manuscript version is made available under the CCBY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Owner
Elsevier Inc.
Copyright Date
2006
Language
en
File Format
application/pdf
Recommended Citation
Chowdhury, Atoshi; Hogben, Leslie; Melancon, Jude; and Mikkelson, Rana, "Rational realization of maximum eigenvalue multiplicity of symmetric tree sign patterns" (2006). Mathematics Publications. 81.
https://lib.dr.iastate.edu/math_pubs/81
Comments
This is a manuscript of an article from Linear Algebra and its Applications 418 (2006): 380, doi:10.1016/j.laa.2006.02.017. Posted with permission.