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2016 | 4 | 1 | 67-72
Tytuł artykułu

Sufficient conditions to be exceptional

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
67-72
Opis fizyczny
Daty
wydano
2016-01-01
otrzymano
2015-04-22
zaakceptowano
2015-11-12
online
2015-12-16
Twórcy
  • Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187
Bibliografia
  • [1] L. D. Baumert, Extreme copositive quadratic forms, Ph.D. Thesis, California Institute of Technology, Pasadena, California, 1965.
  • [2] L. D. Baumert, Extreme copositive quadratic forms, Pacific Journal of Mathematics19(2) (1966) 197-204.[Crossref]
  • [3] L. D. Baumert, Extreme copositive quadratic forms II, Pacific Journal of Mathematics20(1) (1967) 1-20.[Crossref]
  • [4] Z. B. Charles, M. Farber, C. R. Johnson, L. Kennedy-Shaffer, Nonpositive eigenvalues of hollow, symmetric, nonnegative matrices, SIAM Journal of Matrix Anal. Appl.34(3) (2013) 1384-1400.[Crossref][WoS]
  • [5] P. J. C. Dickinson, M. Dür, L. Gijben, R. Hildebrand, Irreducible elements of the copositive cone, Linear Algebra and its Applications439 (2013) 1605-1626.[WoS]
  • [6] R. DeMarr, Nonnegative matrices with nonnegative inverses, Proceedings of the American Mathematical Society35(1) (1972) 307–308.[WoS]
  • [7] P. H. Diananda, On non-negative forms in real variables some or all of which are non-negative, Proc. Cambridge Philosoph. Soc.58 (1962), 17–25.
  • [8] M. Hall, Combinatorial theory, Blaisdell/Ginn, 1967.
  • [9] R. A. Horn and C. R. Johnson, Matrix analysis, Cambridge University Press, 1985.
  • [10] M. Hall and M. Newman, Copositive and completely positive quadratic forms, Proc. Camb. Phil. Soc.59 (1963) 329–339.[Crossref]
  • [11] A. J. Hoffman and F. Pereira, On copositive matrices with −1, 0, 1 entries, Journal of Combinatorial Theory (A)14 (1973) 302–309.
  • [12] C. R. Johnson and R. Reams, Constructing copositive matrices from interior matrices, Electronic Journal of Linear Algebra17 (2008) 9–20.
  • [13] C. R. Johnson and R. Reams, Spectral theory of copositive matrices, Linear Algebra and its Applications395 (2005) 275–281.
  • [14] H. Minc, Nonnegative Matrices, Wiley, New York, 1988.
  • [15] H. Väliaho, Criteria for copositive matrices, Linear Algebra and its Applications81 (1986) 19–34.[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0007
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