On the Characteristic Polynomial and Eigenvectors in Terms of the Tree-Like Structure of a Digraph
- Authors: Buslov V.A.1
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Affiliations:
- St.Petersburg State University
- Issue: Vol 232, No 1 (2018)
- Pages: 6-20
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241249
- DOI: https://doi.org/10.1007/s10958-018-3854-5
- ID: 241249
Cite item
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.
About the authors
V. A. Buslov
St.Petersburg State University
Author for correspondence.
Email: abvabv@bk.ru
Russian Federation, St. Petersburg