Journal ArticleDOI
A simple proof of the Perron-Frobenius theorem for positive symmetric matrices
TLDR
In this paper, an elementary proof is given that the statistical mechanical transfer matrix, when symmetric, has a maximum eigenvalue which is non-degenerate and larger than the absolute value of any other eigen value.Abstract:
An elementary proof is given that the statistical mechanical transfer matrix, when symmetric, has a maximum eigenvalue which is non-degenerate and larger than the absolute value of any other eigenvalue. Moreover, the corresponding eigenvector can be chosen so that all its entire entries are strictly positive.read more
Citations
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Journal ArticleDOI
The Many Proofs and Applications of Perron's Theorem
TL;DR: The many proofs given during the last 93 years are categorized and critiqued (including Perron's original two proofs, and a more natural proof) and this simple-to-understand result of Perron is presented.
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Multivariate Linear Relationships: Maximum Likelihood Estimation and Regression Bounds
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Point Interaction in two and three dimensional Riemannian Manifolds
Fatih Erman,O. Teoman Turgut +1 more
TL;DR: In this paper, a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel is presented.
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Point interactions in two- and three-dimensional Riemannian manifolds
Fatih Erman,O. Teoman Turgut +1 more
TL;DR: In this article, a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac-delta interactions on two-and three-dimensional Riemannian manifolds using the heat kernel is presented.
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The positivity and other properties of the matrix of capacitance: Physical and mathematical implications
TL;DR: In this paper, it was shown that the capacitance in electrostatics is a positive-singular matrix with a non-degenerate null eigenvalue, and the physical implications of this fact were explored.
References
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Book
Introduction to Matrix Analysis
TL;DR: In this article, the Second Edition Preface is presented, where Maximization, Minimization, and Motivation are discussed, as well as a method of Hermite and Quadratic Form Index.
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