Results 21 to 28 of about 169 (28)

Cones and convex bodies with modular face lattices [PDF]

arXiv, 2009
If a convex body C has modular and irreducible face lattice (and is not strictly convex), there is a face-preserving homeomorphism from C to a section of a cone of hermitian matrices or C has dimension 8, 14 or 26.
arxiv  

Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums [PDF]

arXiv, 2009
In this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums. These conditions are variations of Bapat-Raghavan and Franklin-Lorenz conditions.
arxiv  

A Note on the Convex Hull of Finitely Many Projections of Spectrahedra [PDF]

arXiv, 2009
A spectrahedron is a set defined by a linear matrix inequality. A projection of a spectrahedron is often called a semidefinitely representable set. We show that the convex hull of a finite union of such projections is again a projection of a spectrahedron. This improves upon the result of Helton and Nie, who prove the same result in the case of bounded
arxiv  

A new family of representatiosnof virtually free groups [PDF]

arXiv, 2011
We construct a new family of irreducible unitary representations of a finitely generated virtually free group L. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the regular representation, thus implying that all the representations in this family can be realized on the boundary ...
arxiv  

How to project onto the monotone nonnegative cone using Pool Adjacent Violators type algorithms [PDF]

arXiv, 2012
The metric projection onto an order nonnegative cone from the metric projection onto the corresponding order cone is derived. Particularly, we can use Pool Adjacent Violators-type algorithms developed for projecting onto the monotone cone for projecting onto the monotone nonnegative cone too.
arxiv  

Matrices with totally positive powers and their generalizations [PDF]

arXiv, 2013
In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of eventually positive matrices. We mainly focus on the spectral properties of such matrices.
arxiv  

Interiors of completely positive cones [PDF]

arXiv, 2014
A symmetric matrix $A$ is completely positive (CP) if there exists an entrywise nonnegative matrix $B$ such that $A = BB^T$. We characterize the interior of the CP cone. A semidefinite algorithm is proposed for checking interiors of the CP cone, and its properties are studied.
arxiv  

Symmetric Nonnegative 5x5 Matrices Realizing Previously Unknown Region [PDF]

arXiv, 2014
In this paper we present some symmetric nonnegative 5x5 matrix families that realize a previously unknown region. We also prove that these and other symmetric nonnegative 5x5 matrix families are closed under perturbations first presented in W. Guo. Eigenvalues of nonnegative matrices. Linear Algebra and its Applications, 266:261-270, 1997.
arxiv