In this paper we will establish some necessary and/or sufficient conditions for both a nonsingular and a singular matrix A (interpreted as a linear map) to be pseudomonotone. The given results are in terms of the sign of the determinants of the principal submatrices and of the cofactors of A in the nonsingular case and in terms of the structure of A in the singular case. A complete characterization of pseudomonotonicity in terms of the coefficients of a 3 × 3 matrix is given and a method for constructing a merely pseudomonotone matrix is suggested.
Pseudomonotonicity of a Linear Map on the Interior of the Positive Orthant
MARTEIN, LAURA;
2006-01-01
Abstract
In this paper we will establish some necessary and/or sufficient conditions for both a nonsingular and a singular matrix A (interpreted as a linear map) to be pseudomonotone. The given results are in terms of the sign of the determinants of the principal submatrices and of the cofactors of A in the nonsingular case and in terms of the structure of A in the singular case. A complete characterization of pseudomonotonicity in terms of the coefficients of a 3 × 3 matrix is given and a method for constructing a merely pseudomonotone matrix is suggested.File in questo prodotto:
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