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Introduction

Shaun M. Fallat and Charles R. Johnson

in Totally Nonnegative Matrices

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691121574
eISBN:
9781400839018
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691121574.003.0001
Subject:
Mathematics, Applied Mathematics

This introductory chapter is an overview of totally positive (or nonnegative) matrices (TP or TN matrices). Positivity has roots in every aspect of pure, applied, and numerical mathematics. The ... More


Other Related Topics on TN Matrices

Shaun M. Fallat and Charles R. Johnson

in Totally Nonnegative Matrices

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691121574
eISBN:
9781400839018
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691121574.003.0011
Subject:
Mathematics, Applied Mathematics

This chapter reviews a number of subtopics connected with TN matrices; including powers and roots of TN matrices, TP/TN polynomial matrices, subdirect sums of TN matrices, and Perron complements of ... More


Sign Variation of Vectors and TN Linear Transformations

Shaun M. Fallat and Charles R. Johnson

in Totally Nonnegative Matrices

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691121574
eISBN:
9781400839018
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691121574.003.0005
Subject:
Mathematics, Applied Mathematics

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 ... More


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