Sufficient conditions to be exceptional

• Autorzy: Charles R. Johnson , Robert B. Reams
• 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).

Słowa kluczowe

EN

copositive matrix; positive semidefinite; nonnegative matrix; exceptional copositive matrix; irreducible matrix

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 67-72

Daty

wydano

2016-01-01

otrzymano

2015-04-22

zaakceptowano

2015-11-12

online

2015-12-16

Twórcy

autor

Charles R. Johnson

• Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187

autor

Robert B. Reams

• Department of Mathematics, SUNY Plattsburgh, 101 Broad Street, Plattsburgh, NY 12901

Bibliografia

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• [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]

Identyfikatory

DOI

10.1515/spma-2016-0007