The inverse problems of the determinantal regions of ray pattern and complex sign pattern matrices

We study the inverse problems for the determinantal regions R A of the ray pattern matrices and the determinantal regions S A of the complex sign pattern matrices. We determine all, but eight possible exceptions (in two equivalent classes), the determinantal regions S A when A ranges over all comple...

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Bibliographic Details
Published in:Linear algebra and its applications 2006-07, Vol.416 (2), p.835-843
Main Authors: Shao, Jia-Yu, Liu, Yue, Ren, Ling-Zhi
Format: Article
Language:English
Subjects:
Algebra
Complex
Determinant
Exact sciences and technology
Inverse problem
Linear and multilinear algebra, matrix theory
Mathematics
Matrix
Ray pattern
Sciences and techniques of general use
Sign
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Summary:We study the inverse problems for the determinantal regions R A of the ray pattern matrices and the determinantal regions S A of the complex sign pattern matrices. We determine all, but eight possible exceptions (in two equivalent classes), the determinantal regions S A when A ranges over all complex square matrices. We also determine all the possible determinantal regions R A , except those regions which are the union of {0} and an open sector with an angle greater than π. We also answer several questions proposed in [J.-Y. Shao, H.-Y. Shan, The determinantal regions of complex sign pattern matrices and ray pattern matrices, Linear Algebra Appl. 395 (2005) 211–228] concerning the number of the connected components of the set R A ⧹{0} (and of the set S A ⧹{0}).
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2005.12.025