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TP Matrices and TP Completability
Wang, Duo
Wang, Duo
Abstract
A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegative and totally positive (TP) if the determinant of every square submatrix is positive. The TP (TN) completion problem asks which partial matrices have a TP (TN) completion. In this paper, several new TP-completable pat- terns in 3-by-n matrices are identied. The relationship between expansion and completability is developed based on the prior re- sults about single unspecied entry. These results extend our un- derstanding of TP-completable patterns. A new Ratio Theorem related to TP-completability is introduced in this paper, and it can possibly be a helpful tool in TP-completion problems.
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2018-05-01
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Mathematics