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On a bound on algebraic connectivity: the case of equality

Stephen J. Kirkland, Neumann, Michael, Bryan L. Shader (1998)

Czechoslovak Mathematical Journal

In a recent paper the authors proposed a lower bound on $1 - λ_{i}$ , where $λ_{i}$ , $λ_{i} \neq 1$ , is an eigenvalue of a transition matrix $T$ of an ergodic Markov chain. The bound, which involved the group inverse of $I - T$ , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...

On a cell decomposition for Hankel matrices and rational functions.

Diederich Hinrichsen, Wilfried Manthey (1994)

Journal für die reine und angewandte Mathematik

On a class of linear models.

Radu Theodorescu (1985)

Trabajos de Estadística e Investigación Operativa

This paper is concerned with classification criteria, asymptotic behaviour and stationarity of a non-Markovian model with linear transition rule, called a linear OM-chain. This problems are solved by making use of the structure of the stochastic matrix appearing in the definition of such a model. The model studied includes as special cases the Markovian model as well as the linear learning model, and has applications in psychological and biological research, in control theory, and in adaptation...

On a class of matrices which arise in the numerical solution of Euler equations.

Reinhard Nabben (1992)

Numerische Mathematik

On a classic example in the nonnegative inverse eigenvalue problem.

Laffey, Thomas J., Šmigoc, Helena (2008)

ELA. The Electronic Journal of Linear Algebra [electronic only]

On a Companion Operator for Analytic Functions.

G.W. Stewart (1971/1972)

Numerische Mathematik

On a decomposition of square matrices over a ring with identity.

Lüneburg, Heinz (1987)

Séminaire Lotharingien de Combinatoire [electronic only]

On a direct method for the solution of nearly uncoupled Markov chains.

G.W. Stewart, G. Zhang (1991)

Numerische Mathematik

On a generalization of the Van Der Waerden conjecture

Sasser, D.W., Slater, M.L. (1969)

Portugaliae mathematica

On a geometric property of positive definite matrices cone.

Ito, Masatoshi, Seo, Yuki, Yamazaki, Takeaki, Yanagida, Masahiro (2009)

Banach Journal of Mathematical Analysis [electronic only]

On a $J$ -polar decomposition of a bounded operator and matrices of $J$ -symmetric and $J$ -skew-symmetric operators.

Zagorodnyuk, Sergey M. (2010)

Banach Journal of Mathematical Analysis [electronic only]

On a nonnegative irreducible matrix that is similar to a positive matrix

Raphael Loewy (2012)

Open Mathematics

Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.

On a Schur complement inequality for the Hadamard product of certain totally nonnegative matrices.

Yang, Zhongpeng, Feng, Xiaoxia (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

On a strong form of a conjecture of Boyle and Handelman.

Goldberger, Assaf, Neumann, Michael (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

On a surprising relation between the Marchenko–Pastur law, rectangular and square free convolutions

Florent Benaych-Georges (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we prove a result linking the square and the rectangular R-transforms, the consequence of which is a surprising relation between the square and rectangular versions the free additive convolutions, involving the Marchenko–Pastur law. Consequences on random matrices, on infinite divisibility and on the arithmetics of the square versions of the free additive and multiplicative convolutions are given.

On a theorem of Everitt, Thompson, and de Pillis

Miroslav Fiedler, Thomas L. Markham (1994)

Mathematica Slovaca

On an exposed element of a set of doubly stochastic rectangular matrices

Pavel Čihák (1970)

Commentationes Mathematicae Universitatis Carolinae

On asymptotic growth of the support of free multiplicative convolutions.

Kargin, Vladislav (2008)

Electronic Communications in Probability [electronic only]

On Bauer's Generalized Gershgorin Discs.

E. Deutsch, C. Zenger (1975)

Numerische Mathematik

On bilinear forms based on the resolvent of large random matrices

Walid Hachem, Philippe Loubaton, Jamal Najim, Pascal Vallet (2013)

Annales de l'I.H.P. Probabilités et statistiques

Consider a $N \times n$ non-centered matrix $𝛴_{n}$ with a separable variance profile: $𝛴_{n} = \frac{D_{n}^{1 / 2} X_{n} {\tilde{D}}_{n}^{1 / 2}}{\sqrt{n}} + A_{n} .$ Matrices $D_{n}$ and ${\tilde{D}}_{n}$ are non-negative deterministic diagonal, while matrix $A_{n}$ is deterministic, and $X_{n}$ is a random matrix with complex independent and identically distributed random variables, each with mean zero and variance one. Denote by $Q_{n} (z)$ the resolvent associated to $𝛴_{n} 𝛴_{n}^{*}$ , i.e. $Q_{n} (z) = {(𝛴_{n} 𝛴_{n}^{*} - z I_{N})}^{- 1} .$ Given two sequences of deterministic vectors $(u_{n})$ and $(v_{n})$ with bounded Euclidean norms, we study the limiting behavior of the random bilinear form: $u_{n}^{*} Q_{n} (z) v_{n} \forall z \in ℂ - ℝ^{+},$ as the dimensions...

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