Print Email Facebook Twitter Inverse eigenvalue and related problems for hollow matrices described by graphs Title Inverse eigenvalue and related problems for hollow matrices described by graphs Author Dahlgren, F.S. (TU Delft Network Architectures and Services; Georgia State University) Gershkoff, Zachary (Louisiana State University) Hogben, Leslie (Iowa State University; American Institute of Mathematics) Motlaghian, Sara (Georgia State University) Young, Derek (Mount Holyoke College) Date 2022 Abstract A hollow matrix described by a graph G is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in G. For a given graph G, the determination of all possible spectra of matrices associated with G is the hollow inverse eigenvalue problem for G. Solutions to the hollow inverse eigenvalue problems for paths and complete bipartite graphs are presented. Results for related subproblems such as possible ordered multiplicity lists, maximum multiplicity of an eigenvalue, and minimum number of distinct eigenvalues are presented for additional families of graphs. Subject Hollow matrixInverse eigenvalue problemMaximum multiplicityMaximum nullityMinimum number of distinct eigenvaluesMinimum rankOrdered multiplicity list To reference this document use: http://resolver.tudelft.nl/uuid:983fc087-78c1-47ad-bcdb-760dc5b3c169 DOI https://doi.org/10.13001/ela.2022.6941 ISSN 1537-9582 Source The Electronic Journal of Linear Algebra, 38, 661-679 Part of collection Institutional Repository Document type journal article Rights © 2022 F.S. Dahlgren, Zachary Gershkoff, Leslie Hogben, Sara Motlaghian, Derek Young Files PDF vol38_pp661_679.pdf 533.7 KB Close viewer /islandora/object/uuid:983fc087-78c1-47ad-bcdb-760dc5b3c169/datastream/OBJ/view