Nonsingular almost strictly sign regular matrices

作者：Huang, Rong^*; Liu, Jianzhou; Zhu, Li

来源：Linear Algebra and Its Applications, 2012, 436(11): 4179-4192.

DOI：10.1016/j.laa.2012.01.012

• Almost strictly sign regular matrices
• Almost strictly totally positive matrices
• Boundary almost trivial minors

The class of nonsingular almost strictly totally positive matrices has been characterized [M. Gasca, J.M. Pena, 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.

• 出版日期2012-6-1
• 单位湘潭大学