Accession Number:

AD0702869

Title:

INTEGRAL EXTREME POINTS

Descriptive Note:

Technical rept.

Corporate Author:

STANFORD UNIV CA OPERATIONS RESEARCH HOUSE

Report Date:

1967-11-01

Pagination or Media Count:

8.0

Abstract:

It is shown that if A is an integral matrix having linearly independent rows, then the extreme points of the set of nonnegative solutions to Ax b are integral for all integral b if and only if the determinant of every basis matrix is plus or minus 1. This provides a short proof of the Hoffman- Kruskal theorem characterizing unimodular matrices, i.e., matrices in which the determinant of each nonsingular submatrix is plus or minus 1. Their theorem is that if A is integral, then A is unimodular if and only if the extreme points of the set of nonnegative solutions to Ax or b are integral for all integral b.

Subject Categories:

  • Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE