Some Comments about Zero and Non-Zero Eigenvalues from Connected Undirected Planar Graph Adjacency Matrices

Two linear algebra problems implore a solution to them, creating the themes pursued in this paper. The first problem interfaces with graph theory via binary 0-1 adjacency matrices and their Laplacian counterparts. More contemporary spatial statistics/econometrics applications motivate the second pro...

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Bibliographic Details
Published in:AppliedMath 2023-11, Vol.3 (4), p.771-798
Main Author: Griffith, Daniel A.
Format: Article
Language:English
Subjects:
adjacency matrix
eigenvalue
linearly dependent subsets
planar graph
spatial statistics/econometrics
Citations: Items that this one cites
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Summary:Two linear algebra problems implore a solution to them, creating the themes pursued in this paper. The first problem interfaces with graph theory via binary 0-1 adjacency matrices and their Laplacian counterparts. More contemporary spatial statistics/econometrics applications motivate the second problem, which embodies approximating the eigenvalues of massively large versions of these two aforementioned matrices. The proposed solutions outlined in this paper essentially are a reformulated multiple linear regression analysis for the first problem and a matrix inertia refinement adapted to existing work for the second problem.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath3040042