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Pseudomonotonicity of a Linear Map on the Interior of the Positive Orthant

In: Generalized Convexity and Related Topics

Author

Listed:
  • Alberto Cambini

    (University of Pisa)

  • Laura Martein

    (University of Pisa)

Abstract

Summary 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.

Suggested Citation

  • Alberto Cambini & Laura Martein, 2007. "Pseudomonotonicity of a Linear Map on the Interior of the Positive Orthant," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 115-131, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-37007-9_6
    DOI: 10.1007/978-3-540-37007-9_6
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