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Title: On the Characteristic Polynomial and Eigenvectors in Terms of the Tree-Like Structure of a Digraph

Abstract

Regarding a square matrix as the adjacency matrix of a weighted digraph, we construct an extended digraph whose Laplacian contains the original matrix as a submatrix. This construction allows us to use known results on Laplacians to study arbitrary square matrices. The calculation of an eigenvector in a parametric form demonstrates a connection between its components and the tree-like structure of the digraph.

Authors:
 [1]
  1. St.Petersburg State University (Russian Federation)
Publication Date:
OSTI Identifier:
22774017
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 232; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; EIGENVECTORS; GRAPH THEORY; LAPLACIAN; MATRICES; POLYNOMIALS

Citation Formats

Buslov, V. A., E-mail: abvabv@bk.ru, E-mail: v.buslov@spbu.ru. On the Characteristic Polynomial and Eigenvectors in Terms of the Tree-Like Structure of a Digraph. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3854-5.
Buslov, V. A., E-mail: abvabv@bk.ru, E-mail: v.buslov@spbu.ru. On the Characteristic Polynomial and Eigenvectors in Terms of the Tree-Like Structure of a Digraph. United States. doi:10.1007/S10958-018-3854-5.
Buslov, V. A., E-mail: abvabv@bk.ru, E-mail: v.buslov@spbu.ru. Sun . "On the Characteristic Polynomial and Eigenvectors in Terms of the Tree-Like Structure of a Digraph". United States. doi:10.1007/S10958-018-3854-5.
@article{osti_22774017,
title = {On the Characteristic Polynomial and Eigenvectors in Terms of the Tree-Like Structure of a Digraph},
author = {Buslov, V. A., E-mail: abvabv@bk.ru, E-mail: v.buslov@spbu.ru},
abstractNote = {Regarding a square matrix as the adjacency matrix of a weighted digraph, we construct an extended digraph whose Laplacian contains the original matrix as a submatrix. This construction allows us to use known results on Laplacians to study arbitrary square matrices. The calculation of an eigenvector in a parametric form demonstrates a connection between its components and the tree-like structure of the digraph.},
doi = {10.1007/S10958-018-3854-5},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 1,
volume = 232,
place = {United States},
year = {2018},
month = {7}
}