QUADRATIC FORMS SEMI-DEFINITE OVER CONVEX CONES.

Abstract

A differentiable function on a convex set K is said to be K-flat if its gradient vanishes at each of its zeros belonging to K. K-flatness of quadratic forms implies their constrained semi-definiteness. This furnishes a useful characterization of positive semi-definite matrices (when K is the whole space) and 'copositive-plus' matrices (when K is the non-negative orthant). Parallel comparisions between these classes of matrices are made. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 18, 1967
Accession Number
AD0702870

Entities

People

  • C. E. Lemke
  • G. J. Habetler
  • Richard Cottle

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algebra
  • Behavior And Behavior Mechanisms
  • Behavioral Disciplines And Activities
  • Behavioral Sciences
  • Convex Sets
  • Cooperation
  • Group Dynamics
  • Mathematics
  • Set Theory

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research

Technology Areas

  • Space
  • Space - Space Objects