ON POSITIVE PRINCIPAL MINORS

Abstract

The relation between matrices with all principal minors positive and positive definite matrices is explored in the non-symmetric case. It is shown that simple rescaling of rows and columns is insufficient to transform the former into the latter. As a consequence it appears that the class of problems that can be solved by complementary pivot theory of mathematical programming has been non-trivially extended beyond the convex case represented by linear and quadratic programming and takes its place along with another important extension of Lemke and Howson for the matrix associated with bi-matrix games.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1967
Accession Number
AD0649630

Entities

People

  • George Bernard Dantzig

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Computer Programming
  • Contracts
  • Governments
  • Instructions
  • Interdisciplinary Science
  • Mathematical Programming
  • Mathematics
  • Matrix Theory
  • Military Research
  • Nonconvex Programming
  • Operations Research
  • Quadratic Programming
  • Theorems
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research
  • Theoretical Analysis.