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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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Recognition

Recognition

Chapter:
(p.73) Chapter Three Recognition
Source:
Totally Nonnegative Matrices
Author(s):

Shaun M. Fallat

Charles R. Johnson

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691121574.003.0004

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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