On copositive matrices with −1, 0, 1 entries
TLDR
It is given a counterexample to a conjecture of L. D. Baumert about zeros of copositive matrices and those matrices in E which are on extreme rays of the cone ofCopositiveMatrices which are positive semidefinite, respectively.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-05-01 and is currently open access. It has received 56 citations till now. The article focuses on the topics: Copositive matrix.read more
Citations
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Journal ArticleDOI
A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas
TL;DR: This is a bibliography of signed graphs and related mathematics, where work on weighted graphs are regarded as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".
Book ChapterDOI
Copositive Programming – a Survey
TL;DR: The purpose of this survey is to introduce the field to interested readers in the optimization community who wish to get an understanding of the basic concepts and recent developments inCopositive programming, including modeling issues and applications, the connection to semidefinite programming and sum-of-squares approaches, as well as algorithmic solution approaches for copositive programs.
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A Variational Approach to Copositive Matrices
TL;DR: This work surveys essential properties of the so-called copositive matrices, the study of which has been spread over more than fifty-five years, with special emphasis on variational aspects related to the concept of copositivity.
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Inverse M-matrices☆
TL;DR: In this paper, a comprehensive expository study of nonnegative matrices which happen to be inverses of M-matrices is presented, aimed at an audience conversant with basic ideas of matrix theory.
Journal ArticleDOI
On copositive matrices
TL;DR: In this article, a criterion for copositive matrices is given and for n = 3 the set of all copositives is determined in terms of matrix elements, and the problem of excluding periodic solutions of certain algebraic differential equations is considered.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Journal ArticleDOI
Bimatrix Equilibrium Points and Mathematical Programming
TL;DR: In this paper, simple constructive proofs are given of solutions to the matric matric system Mz − ω = q; z ≧ 0; ω ≧ 1; zT = 0, for various kinds of data M, q, which embrace quadratic programming and the problem of finding equilibrium points of bimatrix games.
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Maxima for Graphs and a New Proof of a Theorem of Turán
T. S. Motzkin,E. G. Straus +1 more
TL;DR: In this article, the maximum of a square-free quadratic form on a simplex was investigated and the following question was suggested by a problem of J. E. MacDonald Jr.
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Complementary pivot theory of mathematical programming
TL;DR: The role of problems of the form w and z satisfying w = q + Mz, w = or 0, z = or0, zw = 0 play a fundamental role in mathematical programming.