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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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Determinantal Inequalities for TN Matrices

Determinantal Inequalities for TN Matrices

(p.129) Chapter Six Determinantal Inequalities for TN Matrices
Totally Nonnegative Matrices

Shaun M. Fallat

Charles R. Johnson

Princeton University Press

This chapter begins an investigation into the possible relationships among the principal minors of TN matrices. An important goal is to examine all the inequalities among the principal minors of TN matrices. More generally, this chapter also studies families of determinantal inequalities that hold for all TN matrices. The intention here is to employ certain ideas pertinent to theory of TN matrices to derive a description with respect to positive semidefinite matrices. One notable difference between the class of TN matrices and the positive semidefinite matrices is that TN matrices are not in general closed under the simultaneous permutation of rows and columns, while positive semidefinite matrices are closed under such an operation.

Keywords:   determinantal inequalities, principal minors, positive semidefinite matrices, TN matrices

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