On the change of the Jordan form under the transition from the adjacency matrix of a vertex-transitive digraph to its principal submatrix of co-order one

DOI10.1016/j.laa.2004.07.010zbMath1066.15011OpenAlexW2068443794MaRDI QIDQ1765897

Sergey V. Savchenko

Publication date: 23 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2004.07.010

zbMATH Keywords

eigenvalueJordan canonical formadjacency matrixJordan blockJordan chainvertex-transitive digraph

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Directed graphs (digraphs), tournaments (05C20) Canonical forms, reductions, classification (15A21)

Related Items (4)

Eigenvalues of Cayley graphs ⋮ Normal matrices and their principal submatrices of co-order one ⋮ An efficient Jordan basis algorithm ⋮ Spectra of digraphs

Cites Work

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• Extensions of Jordan bases for invariant subspaces of a matrix
• Cayley digraphs with normal adjacency matrices
• Eigenvalues of graphs and digraphs
• Interlacing inequalities for invariant factors
• Imbedding conditions for \(\lambda\)-matrices
• On the Perron roots of principal submatrices of co-order one of irreducible nonnegative matrices
• A graph polynomial and its applications
• Arc transitive covering digraphs and their eigenvalues
• On Groups with Two Triply Transitive Permutation Representations

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