On a sign-pattern matrix and it's related algorithms for L-matrix

  • Seol, Han-Guk (Department of Mathematics SungKyunKwan University) ;
  • Kim, Yu-Hyuk (Department of Mathematics SungKyunKwan University) ;
  • Lee, Sang-Gu (Department of Mathematics SungKyunKwan University)
  • Published : 1999.06.30

Abstract

A real $m{\times}n$ matrix A is called an L-matrix if every matrix in its qualitative class has linearly independent rows. Since the number of the sign pattern matrices of the given size is finite, we can list all patterns lexicographically. In [2], a necessary and sufficient condition for a matrix to be an L-matrix was given. We presented an algorithm which decides whether the given matrix is an L-matrix or not. In this paper, we develope an algorithm and C-program which will determine whether a given matrix is an L-matrix or not, or an SNS-matrix or not. In addition, we have extended our algorithm to be able to classify sign-pattern matrices, and to find barely L-matrices from a given matrix and to list all $m{\times}n$ L-matrices.

Acknowledgement

Supported by : Ministry of Education