Date of Award

12-11-2017

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Frank Hall

Second Advisor

Zhongshan Li

Abstract

This thesis builds upon the results in “G-matrices, J-orthogonal matrices, and their sign patterns”, Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloˇzn ́ık. Some general results about the sign patterns of J-orthogonal matrices are proved, including about block diagonal matrices. It is shown that every full 4 × 4 sign pattern allows J -orthogonality and as a result that, for n ≤ 4, all n × n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. The 3 × 3 sign patterns of the J -orthogonal matrices which have zero entires are also characterized.

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