A CONDITION FOR THE STRONG REGULARITY OF MATRICES IN THE MINIMAX ALGEBRA

被引：30

作者：

BUTKOVIC, P

HEVERY, F

机构：

[1] Univ Pavla Jozefa Safarika, Katedra, Geometrie a Algebry, Kosice, Czech, Univ Pavla Jozefa Safarika, Katedra Geometrie a Algebry, Kosice, Czech

来源：

DISCRETE APPLIED MATHEMATICS | 1985年 / 11卷 / 03期

关键词：

D O I：

10.1016/0166-218X(85)90073-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Columns of a matrix A in the minimax algebra are called strongly linearly independent if for some b the system equations A multiplied by x equals b is uniquely solvable. This paper presents a condition which is necessary and sufficient for the strong linear independence of columns of a given matrix in the minimax algebra based on a dense linearly ordered commutative group. In the case of square matrices an O(n**3) method for checking this property as well as for finding at least one b such that A multiplied by x equals b is uniquely solvable is derived. A connection with the classical assignment problem is formulated.

引用

页码：209 / 222

页数：14