COMPLETION FOR TIGHT SIGN-CENTRAL MATRICES

Title & Authors
COMPLETION FOR TIGHT SIGN-CENTRAL MATRICES
Cho, Myung-Sook; Hwang, Suk-Geun;

Abstract
A real matrix A is called a sign-central matrix if for, every matrix $\small{\tilde{A}}$ with the same sign pattern as A, the convex hull of columns of $\small{\tilde{A}}$ contains the zero vector. A sign-central matrix A is called a tight sign-central matrix if the Hadamard (entrywise) product of any two columns of A contains a negative component. A real vector x = $\small{(x_1,{\ldots},x_n)^T}$ is called stable if $\small{\|x_1\|{\leq}\|x_2\|{\leq}{\cdots}{\leq}\|x_n\|}$. A tight sign-central matrix is called a $\small{tight^*}$ sign-central matrix if each of its columns is stable. In this paper, for a matrix B, we characterize those matrices C such that [B, C] is tight ($\small{tight^*}$) sign-central. We also construct the matrix C with smallest number of columns among all matrices C such that [B, C] is $\small{tight^*}$ sign-central.뤞덐렶⨀⨀㼞⨀줗̀삹ﶖ⨀傗ꐂ̀삹ﶖ⨀႘ꐂ
Keywords
sign-central mztrix;tight sign-central matrix;
Language
English
Cited by
References
1.
T. Ando and R. A. Brualdi, Sign-central matrices, Linear Algebra Appl. 208/209 (1994), 283-295

2.
R. A. Brualdi and B. L. Shader, Matrices of sign-solvable linear systems, Cambride Tracts in Mathematics 116, Cambridge University Press, New York, 1995

3.
S.-G. Hwang, I.-P. Kim, S.-J. Kim and X. D. Zhang, Tight sign-central matrices, Linear Algebra Appl. 371 (2003), 225-240

4.
S.-G. Hwang, I.-P. Kim, S.-J. Kim and S.-G. Lee, The number of zeros of a tight sign-central matrix, Linear Algebra Appl. 407 (2005), 296-310