Chapter 42
Sign Pattern Matrices
Frank J. Hall
Georgia State University
Zhongshan Li
Georgia State University
The origins of sign pattern matrices are in the book [Sam47] by the Nobel Economics Prize winner P. Samuelson, who pointed to the need to solve certain problems in economics and other areas based only on the signs of the entries of the matrices. The study of sign pattern matrices has become somewhat synonymous with qualitative matrix analysis. The dissertation of C. Eschenbach [Esc87], directed by C.R. Johnson, studied sign pattern matrices that “require” or “allow” certain properties and summarized some of the work on sign patterns up to that point. In 1995, Richard Brualdi and Bryan Shader produced a thorough treatment [BS95] on sign ...
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