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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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Hadamard Products and Powers of TN Matrices

Hadamard Products and Powers of TN Matrices

Chapter:
(p.167) Chapter Eight Hadamard Products and Powers of TN Matrices
Source:
Totally Nonnegative Matrices
Author(s):

Shaun M. Fallat

Charles R. Johnson

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691121574.003.0009

This chapter introduces the Hadamard (or entrywise) product and offers a survey of the known results pertaining to Hadamard products of TN matrices, including a note on Hadamard powers. The well-known fact that TP matrices are not closed under Hadamard multiplication has certainly not deterred researchers from this interesting topic. In fact, it can be argued that this has fueled considerable investigations on when such closure issues, with particular attention being paid to specific subclasses of TP/TN matrices. Hence, the chapter first defines and denotes the Hadamard product of two m-by-n matrices A = [asubscript ij] and B = [bsubscript ij] before turning to a number of concepts connected with Hadamard products and Hadamard powers of TPₖ matrices.

Keywords:   Hadamard products, Hadamard powers, Hadamard multiplication, Hadamard core

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