Results 41 to 50 of about 448 (54)
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
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
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
Refined inertias of positive and hollow positive patterns
Special MatricesWe investigate refined inertias of positive patterns and patterns that have each off-diagonal entry positive and each diagonal entry zero, i.e., hollow positive patterns. For positive patterns, we prove that every refined inertia (n+,n−,nz,2np)\left({n}_{
Berliner Adam H. +3 more
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Matrices having a positive determinant and all other minors nonpositive
Special MatricesThe class of square matrices of order nn having a positive determinant and all their minors up to order n−1n-1 nonpositive is considered. A characterization of these matrices based on the Cauchon algorithm is presented, which provides an easy test for ...
Hassuneh Imad +2 more
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The totally nonnegative part of G/P is a ball
, 2019 We show that the totally nonnegative part of a partial flag variety (in the sense of Lusztig) is homeomorphic to a closed ball.Comment: 6 pages. v2: Proof of Lemma 1 moved to arXiv:1707.02010.
Galashin, Pavel +2 more
core
On Complex Matrix-Variate Dirichlet Averages and Its Applications in Various Sub-Domains. [PDF]
Entropy (Basel), 2023 Thankamani P, Sebastian N, Haubold HJ.
europepmc +1 more source
, 2017 This paper explicitly details the relation between $M$-matrices, nonnegative roots of nonnegative matrices, and the embedding problem for finite-state stationary Markov chains.
Van-Brunt, Alexander
core
Monotonicity of the number of positive entries in nonnegative matrix powers. [PDF]
J Inequal Appl, 2018 Xie Q.
europepmc +1 more source
On a nonnegative irreducible matrix that is similar to a positive matrix
Open Mathematics, 2012 Loewy Raphael
doaj +1 more source