20.500.12556/RUL-148518 Distinct eigenvalues are realizable with generic eigenvectors Motivated by applications in matrix constructions used in the inverse eigenvalue problem for graphs, we study a concept of genericity for eigenvectors associated with a given spectrum and a connected graph. This concept generalizes the established notion of a nowhere-zero eigenbasis. Given any simple graph G on n vertices and any spectrum with no multiple eigenvalues, we show that the family of eigenbases for symmetric matrices with this graph and spectrum is generic, strengthening a result of Monfared and Shader. We illustrate applications of this result by constructing new achievable ordered multiplicity lists for partial joins of graphs and providing several families of joins of graphs that are realizable by a matrix with only two distinct eigenvalues. symmetric matrix join of graphs inverse eigenvalue problem minimal number of distinct eigenvalues simetrična matrika spoj grafov inverzni problem lastnih vrednosti najmanjše število različnih lastnih vrednosti true false true Angleški jezik Slovenski jezik Članek v reviji 2023-08-25 08:50:17 2023-08-25 08:50:18 2024-03-01 11:17:37 0000-00-00 00:00:00 2023 0 0 Str. 1-15 no. Vol. 2023 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2023-01-01 51 0308-1087 10.1080/03081087.2023.2232090 162220803 Distinct_eigenvalues_are_realizable_with_generic_eigenvectors.pdf Distinct_eigenvalues_are_realizable_with_generic_eigenvectors.pdf 1 CA96725CE9396E0DE168545B00AE3CAA 371e9870b4d4febc74fa81e03a2eec178c2798f0ff93fa8810fba3fd7cd1a53b b2f20bb0-4334-11ee-b9d7-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=172787 https://www.tandfonline.com/doi/full/10.1080/03081087.2023.2232090 1 972e854c-4313-11ee-b9d7-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=172774 Fakulteta za računalništvo in informatiko 0 0 0