Almost N-matrices and linear complementarity

Abstract An almost N-matrix A is one with real entries whose determinant is positive and proper principal minors are negative. In this paper we obtain some characterization results for almost N-matrices that are similar to N-matrices. Among other things we show that an almost N-matrix of first category with n ⩾4 belongs to the class of Q-matrices. As an application we derive a new univalence result.

[1]  Romesh Saigal,et al.  A Characterization of the Constant Parity Property of the Number of Solutions to the Linear Complementarity Problem , 1972 .

[2]  M. Kojima,et al.  On the number of solutions to a class of linear complementarity problems , 1979, Math. Program..

[3]  D. Gale,et al.  The Jacobian matrix and global univalence of mappings , 1965 .

[4]  Ken-ichi Inada,et al.  The Production Coefficient Matrix and the Stolper-Samuelson Condition , 1971 .

[5]  G. Rota.  Non-negative matrices in the mathematical sciences: A. Berman and R. J. Plemmons, Academic Press, 1979, 316 pp. , 1983 .

[6]  T. Parthasarathy,et al.  On global univalence theorems , 1983 .

[7]  On constructions of partially nonpositive matrices , 1989 .

[8]  M. Shubik,et al.  Convex structures and economic theory , 1968 .

[9]  J. Maybee.  Some Aspects of the Theory of $PN$-Matrices , 1976 .

[10]  S. Karamardian,et al.  The complementarity problem , 1972, Math. Program..

[11]  A. Berman.  Matrices and the linear complementarity problem , 1981 .

[12]  R. Saigal.  On the Alass of Complementary Cones and Lemke’s Algorithm , 1972 .

[13]  David Gale.  The theory of linear economic models , 1960 .

[14]  L. Watson,et al.  Q-matrices and spherical geometry , 1979 .

[15]  L. Watson.  Some Perturbation Theorems for Q-Matrices , 1976 .

[16]  K. Fan.  Some matrix inequalities , 1966 .

[17]  L. Watson,et al.  Erratum: Some Perturbation Theorems for Q-Matrices , 1978 .

[18]  T. Ważewski,et al.  Sur l'évaluation du domaine d'existence des fonctions implicites réelles ou complexes , 1948 .

[19]  S. R. Mohan,et al.  On characterizing N-matrices using linear complementarity , 1992 .

[20]  Gregery A. Johnson,et al.  A generalization of N-matrices☆ , 1982 .