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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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Row and Column Inclusion and the Distribution of Rank

Row and Column Inclusion and the Distribution of Rank

Chapter:
(p.153) Chapter Seven Row and Column Inclusion and the Distribution of Rank
Source:
Totally Nonnegative Matrices
Author(s):

Shaun M. Fallat

Charles R. Johnson

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691121574.003.0008

This chapter contains a detailed account of the distribution of rank deficient submatrices within a TN matrix, including a discussion of the important notion of row and column inclusion. The distribution of ranks among submatrices of a TN matrix is much less free than in a general matrix. Rank deficiency of submatrices in certain positions requires rank deficiency elsewhere. Whereas, in the case of general matrices, rank deficiency of a large submatrix can imply rank deficiency of smaller, included submatrices, in the TN case rank deficiency of small submatrices can imply that of much larger ones. The chapter discusses this and other related phenomenon.

Keywords:   TN matrix, rank deficient submatrices, rank deficiency

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