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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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(p.73) Chapter Three Recognition
Totally Nonnegative Matrices

Shaun M. Fallat

Charles R. Johnson

Princeton University Press

This chapter discusses the recognition of TN matrices. It touches on one of the many applications for the structure of TN matrices. TN matrices enjoy tremendous structure, as a result of requiring all minors to be nonnegative. This intricate structure makes it easier to determine when a matrix is TP than to check when it is a P-matrix, which formally involves far fewer minors. Vandermonde matrices arise in the problem of determining a polynomial of degree at most n − 1 that interpolates n data points. Suppose that n data points (xᵢ,yᵢ)unconverted formula are given. The goal is to construct a polynomial p(x) = a₀ + ax + … + asubscript n − 1xsuperscript n − 1 that satisfies p(xᵢ) = yᵢ for i = 1, 2, …,n.

Keywords:   recognition, TN matrix structure, Vandermonde matrices, positive minors, TP intervals

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