Jump to ContentJump to Main Navigation
Totally Nonnegative Matrices$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 25 May 2020

Sign Variation of Vectors and TN Linear Transformations

Sign Variation of Vectors and TN Linear Transformations

(p.87) Chapter Four Sign Variation of Vectors and TN Linear Transformations
Totally Nonnegative Matrices

Shaun M. Fallat

Charles R. Johnson

Princeton University Press

This chapter develops an array of results about TP/TN matrices and sign variation diminution, along with appropriate converses. If the entries of a vector represent a sampling of consecutive function values, then a change in the sign of consecutive vector entries corresponds to the important event of the (continuous) function passing through zero. It has been known that as a linear transformation, a TP matrix cannot increase the number of sign changes in a vector. The transformations that never increase the number of sign variations are of interest in a variety of applications, including approximation theory and shape preserving transforms, and are of mathematical interest as well.

Keywords:   TN linear transformations, sign variation diminution, vectors, linear transformations, TP matrix, EB factorization

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.