Results 11 to 20 of about 10,069,733 (332)
Skew characteristic polynomial of graphs and embedded graphs [PDF]
Communications in Mathematics, 2022 We introduce a new one-variable polynomial invariant of graphs, which we call the skew characteristic polynomial. For an oriented simple graph, this is just the characteristic polynomial of its anti-symmetric adjacency matrix.
Riya Dogra +3 more
semanticscholar +2 more sources
Efficient computation of the characteristic polynomial [PDF]
Proceedings of the 2005 international symposium on Symbolic and algebraic computation, 2005 This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. We first present two algorithms for the finite fields: one is based on Krylov iterates and Gaussian elimination. We compare it to an improvement of the second algorithm of Keller-Gehrig.
Jean-Guillaume Dumas +2 more
core +4 more sources
How Good Can the Characteristic Polynomial Be for Correlations? [PDF]
International Journal of Molecular Sciences, 2007 The aim of this study was to investigate the characteristic polynomials resulting from the molecular graphs used as molecular descriptors in the characterization of the properties of chemical compounds.
Sorana D Bolboacă +2 more
exaly +3 more sources
Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach. [PDF]
J Phys Chem Lett, 2023 The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs.
Wang TY, Neville SP, Schuurman MS.
europepmc +2 more sources
Chordal graphs and the characteristic polynomial
Discrete Mathematics, 2003 The greedoid ``characteristic polynomial'' is studied for greedoids (anitmatroids, in this case) which arise from chordal graphs. The greedoid two-variable ``Tutte polynomial'' of Gordon and McMahon is, for a greedoid on \(E\) having rank function \(r\), \[ f(t,z) = \sum_{S \subseteq E} t^{r(E) - r(S)} z^{|A|- r(A)}.
Elizabeth W. McMahon +2 more
openaire +3 more sources
Characteristic Polynomial [PDF]
New Frontiers in Nanochemistry, 2020 L. Jäntschi, Sorana D. Bolboacă
semanticscholar +2 more sources
The characteristic polynomial and the matchings polynomial of a weighted oriented graph
, 2012 Let G σ be a weighted oriented graph with skew adjacency matrix S ( G σ ) . Then G σ is usually referred as the weighted oriented graph associated to S ( G σ ) .
S. Gong, Guang-Hui Xu
semanticscholar +2 more sources
On the Characteristic Polynomial of the Eigenvalue Moduli of Random Normal Matrices [PDF]
Constructive approximation, 2022 We study the characteristic polynomial pn(x)=∏j=1n(|zj|-x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Sunggyu Byun, C. Charlier
semanticscholar +1 more source
Random symmetric matrices: rank distribution and irreducibility of the characteristic polynomial [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2021 Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$ -matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main innovation
Asaf Ferber +3 more
semanticscholar +1 more source
Sparse matrices: convergence of the characteristic polynomial seen from infinity [PDF]
Electronic Journal of Probability, 2021 We prove that the reverse characteristic polynomial det(In − zAn) of a random n×nmatrixAn with iidBernoulli(d/n) entries converges in distribution towards the random infinite product ∞ ∏ `=1 (1− z)` where Y` are independent Poisson(d/`) random variables.
S. Coste
semanticscholar +1 more source