Results 21 to 30 of about 419 (42)

Pure states proof of the Matrix-valued P\'olya Positivstellensatz

, 2023
Let $\Sigma$ denote the linear form $x_1 + \cdots + x_n$. By a classical Positivstellensatz of P\'olya, if a real form $f$ is strictly positive on the standard simplex, then $\Sigma^m f$ has strictly positive coefficients for some nonnegative integer $m$.
Tan, Colin
core  

Notes and counterexamples on positive (semi) definite properties of some matrix products

Ain Shams Engineering Journal, 2018
In the present paper, we give some notes and counterexamples to show that the positive (semi) definite property of the Khatri-Rao and Tracy-Singh products of partitioned matrices are in general incorrect and show also that the matrix triangle inequality ...
Zeyad Al-Zhour
doaj   +1 more source

The critical exponent for generalized doubly nonnegative matrices

, 2016
It is known that the critical exponent (CE) for conventional, continuous powers of $n$-by-$n$ doubly nonnegative (DN) matrices is $n-2$. Here, we consider the larger class of diagonalizable, entry-wise nonnegative $n$-by-$n$ matrices with nonnegative ...
Han, Xuchen, Johnson, Charles, Paparella, Pietro   +2 more
core   +1 more source

Completely positive matrices over Boolean algebras and their CP-rank

Special Matrices, 2015
Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite ...
Mohindru Preeti
doaj   +1 more source

Singular M-matrices which may not have a nonnegative generalized inverse

Special Matrices, 2014
A matrix A ∈ ℝn×n is a GM-matrix if A = sI − B, where 0 < ρ(B) ≤ s and B ∈WPFn i.e., both B and Bthave ρ(B) as their eigenvalues and their corresponding eigenvector is entry wise nonnegative.
Sushama Agrawal N., Premakumari K., Sivakumar K.C.   +2 more
doaj   +1 more source

Asymptotic behaviour of random tridiagonal Markov chains in biological applications

, 2012
Discrete-time discrete-state random Markov chains with a tridiagonal generator are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors.
A. E. Hutzenthaler, A. Leizarowitz, B. Noble, B. S. Thomson, D. J. Hartfiel, D. J. Hartfiel, D. N. Cheban, D. Wodarz, E. Asarin, H. Cohn, I. Chueshov, I. Chueshov, J. Wolfowitz, J.-P. Aubin, L. Arnold, L. J. S. Allen, M. A. Krasnosel$'$skij, M. F. Barnsley, M. Neumann, P. E. Kloeden, P. Imkeller, P. J. Bushell   +21 more
core   +1 more source

Hyponormality on a weighted Bergman space of an annulus with a general harmonic symbol

Open Mathematics
In this work we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a logarithmic weight. We give necessary conditions when the symbol is of the form φ+ψ̄ $\varphi +\bar{\psi }$ where both φ and ψ are analytic on ...
Sadraoui Houcine, Halouani Borhen
doaj   +1 more source

Perron Spectratopes and the Real Nonnegative Inverse Eigenvalue Problem

, 2015
Call an $n$-by-$n$ invertible matrix $S$ a \emph{Perron similarity} if there is a real non-scalar diagonal matrix $D$ such that $S D S^{-1}$ is entrywise nonnegative.
Johnson, Charles R., Paparella, Pietro
core   +1 more source

Simple expressions for the long walk distance

, 2012
The walk distances in graphs are defined as the result of appropriate transformations of the $\sum_{k=0}^\infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a connected weighted graph and $t$ is a sufficiently small positive ...
Bapat, Bapat, Chebotarev, Chebotarev, Chebotarev, Harary, Katz, Klein, Meyer, Meyer, Pavel Chebotarev, R. Balaji, R.B. Bapat, Rao, Styan   +14 more
core   +1 more source

Support-based lower bounds for the positive semidefinite rank of a nonnegative matrix [PDF]

, 2013
The positive semidefinite rank of a nonnegative $(m\times n)$-matrix~$S$ is the minimum number~$q$ such that there exist positive semidefinite $(q\times q)$-matrices $A_1,\dots,A_m$, $B_1,\dots,B_n$ such that $S(k,\ell) = \mbox{tr}(A_k^* B_\ell)$.
Dirk, Oliver Theis, Troy Lee
core