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Totally Nonnegative Matrices$
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Shaun M. Fallat and Charles R. Johnson

Print publication date: 2011

Print ISBN-13: 9780691121574

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691121574.001.0001

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Preliminary Results and Discussion

Preliminary Results and Discussion

(p.27) Chapter One Preliminary Results and Discussion
Totally Nonnegative Matrices

Shaun M. Fallat

Charles R. Johnson

Princeton University Press

This chapter lays out a number of basic and fundamental properties of TN matrices along with a compilation of facts and results from core matrix theory that are useful for further development of this topic. Along with the elementary bidiagonal factorization, the rules for manipulating determinants and special determinantal identities constitute the most useful tools for understanding TN matrices. Some of this technology is simply from elementary linear algebra, but the less well-known identities are given here for reference. In addition, other useful background facts are entered into the record, and a few elementary and frequently used facts about TN matrices are presented.

Keywords:   TN matrices, core matrix theory, bidiagonal factorization, determinantal identities, detemrinants, elementary linear algebra

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