Nonsingular almost strictly sign regular matrices

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• 作者：Rong Huang ; ¹ ; ^{rongh98@yahoo.cn} ; Jianzhou Liu² ; Li Zhu ^{liujz@xtu.edu.cn zhuli@xtu.edu.cn}
• 关键词：15A18 ; 15A42 ; 15A57
• 刊名：Linear Algebra and its Applications
• 出版年：2012
• 期刊代码：38_00243795
• 类别：mt
• 出版时间：1 June, 2012
• 卷：436
• 期：11
• 页码：4179-4192
• 文件大小：300 K

摘要

The class of nonsingular almost strictly totally positive matrices has been characterized [M. Gasca, J.M. Pe帽a, Characterizations and decompositions of almost strictly positive matrices, SIAM J. Matrix Anal. Appl. 28 (2006) 1-8]. In this paper, we discuss the class of almost strictly sign regular matrices that includes almost strictly totally positive matrices. A characterization is provided for these matrices in terms of their nontrivial minors using consecutive rows and consecutive columns. In particular, we present a characterization of certain almost strictly sign regular matrices in terms of a very reduced number of boundary almost trivial minors.