Geometric Parter-Wiener, etc. theory

DOI10.1016/j.laa.2017.09.035zbMath1376.15030OpenAlexW2762557863MaRDI QIDQ1675672

Carlos M. Saiago, Charles R. Johnson

Publication date: 2 November 2017

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2017.09.035

zbMATH Keywords

treeeigenvalueHermitian matricesgeometric multiplicitymaximum multiplicitygeneral matrixParter vertex

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (7)

Further generalization of symmetric multiplicity theory to the geometric case over a field ⋮ Change in vertex status after removal of another vertex in the general setting ⋮ The effect of perturbation of an off-diagonal entry pair on the geometric multiplicity of an eigenvalue ⋮ The minimum number of eigenvalues of multiplicity one in a diagonalizable matrix, over a field, whose graph is a tree ⋮ Classification of edges in a general graph associated with the change in multiplicity of an eigenvalue ⋮ The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree ⋮ Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments

Cites Work

• Unnamed Item
• Spectral multiplicity and splitting results for a class of qualitative matrices
• Converse to the Parter--Wiener theorem: the case of non-trees
• Diameter minimal trees
• The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
• The Parter--Wiener Theorem: Refinement and Generalization
• On the minimum number of distinct eigenvalues for a symmetric matrix whose graph is a given tree
• On the Eigenvalues and Eigenvectors of a Class of Matrices

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