On vector configurations that can be realized in the cone of positive matrices
نویسنده
چکیده
Let $v_1$,..., $v_n$ be $n$ vectors in an inner product space. Can we find a natural number $d$ and positive (semidefinite) complex matrices $A_1$,..., $A_n$ of size $d imes d$ such that ${ m Tr}(A_kA_l)= $ for all $k,l=1,..., n$? For such matrices to exist, one must have $ geq 0$ for all $k,l=1,..., n$. We prove that if $n FRENKEL, Peter Erno, WEINER, Mihály. On vector configurations that can be realized in the cone of positive matrices. 2010, 8 p.
منابع مشابه
Gyrovector Spaces on the Open Convex Cone of Positive Definite Matrices
In this article we review an algebraic definition of the gyrogroup and a simplified version of the gyrovector space with two fundamental examples on the open ball of finite-dimensional Euclidean spaces, which are the Einstein and M"{o}bius gyrovector spaces. We introduce the structure of gyrovector space and the gyroline on the open convex cone of positive definite matrices and explore its...
متن کاملInvestigating the Effects of Hardware Parameters on Power Consumptions in SPMV Algorithms on Graphics Processing Units (GPUs)
Although Sparse matrix-vector multiplication (SPMVs) algorithms are simple, they include important parts of Linear Algebra algorithms in Mathematics and Physics areas. As these algorithms can be run in parallel, Graphics Processing Units (GPUs) has been considered as one of the best candidates to run these algorithms. In the recent years, power consumption has been considered as one of the metr...
متن کاملAN OPTIMIZATION-BASED COMPARATIVE STUDY OF DOUBLE LAYER GRIDS WITH TWO DIFFERENT CONFIGURATIONS USING CUCKOO SEARCH ALGORITHM
This paper is concerned with the economical comparison between two commonly used configurations for double layer grids and determining their optimum span-depth ratio. Two ranges of spans as small and big sizes with certain bays of equal length in two directions and various types of element grouping are considered for each type of square grids. In order to carry out a precise comparison between ...
متن کاملOn the topological equivalence of some generalized metric spaces
The aim of this paper is to establish the equivalence between the concepts of an $S$-metric space and a cone $S$-metric space using some topological approaches. We introduce a new notion of a $TVS$-cone $S$-metric space using some facts about topological vector spaces. We see that the known results on cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained from...
متن کاملChapter 8 Copositive Programming
A symmetric matrix S is copositive if yT S y≥0 for all y≥0, and the set of all copositive matrices, denoted C∗, is a closed, pointed, convex cone; see [25] for a recent survey. Researchers have realized how to model many NP-hard optimization problems as copositive programs, that is, programs over C∗ for which the objective and all other constraints are linear [7, 9, 13, 16, 32–34]. This makes c...
متن کامل