Totally nonnegative matrices /

Totally nonnegative matrices /

Saved in:
Bibliographic Details
Author / Creator:FALLAT, SHAUN M.
Imprint:Princeton : Princeton University Press, 2011.
Description:1 online resource.
Language:English
Series:Princeton series in applied mathematics
Subject:
Non-negative matrices.
Non-negative matrices.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8391737
Hidden Bibliographic Details
Other authors / contributors:Johnson, Charles R.
ISBN:1400839017 (electronic bk.)
9781400839018 (electronic bk.)
Notes:Description based on print version record.
Includes bibliographic references (p. [219]-238) and index.
Other form:Original 9780691121574 0691121575
Table of Contents:
  • List of Figures
  • Preface
  • Chapter 0. Introduction
  • 0.0. Definitions and Notation
  • 0.1. Jacobi Matrices and Other Examples of TN matrices
  • 0.2. Applications and Motivation
  • 0.3. Organization and Particularities
  • Chapter 1. Preliminary Results and Discussion
  • 1.0. Introduction
  • 1.1. The Cauchy-Binet Determinantal Formula
  • 1.2. Other Important Determinantal Identities
  • 1.3. Some Basic Facts
  • 1.4. TN and TP Preserving Linear Transformations
  • 1.5. Schur Complements
  • 1.6. Zero-Nonzero Patterns of TN Matrices
  • Chapter 2. Bidiagonal Factorization
  • 2.0. Introduction
  • 2.1. Notation and Terms
  • 2.2. Standard Elementary Bidiagonal Factorization: Invertible Case
  • 2.3. Standard Elementary Bidiagonal Factorization: General Case
  • 2.4. LU Factorization: A consequence
  • 2.5. Applications
  • 2.6. Planar Diagrams and EB factorization
  • Chapter 3. Recognition
  • 3.0. Introduction
  • 3.1. Sets of Positive Minors Sufficient for Total Positivity
  • 3.2. Application: TP Intervals
  • 3.3. Efficient Algorithm for testing for TN
  • Chapter 4. Sign Variation of Vectors and TN Linear Transformations
  • 4.0. Introduction
  • 4.1. Notation and Terms
  • 4.2. Variation Diminution Results and EB Factorization
  • 4.3. Strong Variation Diminution for TP Matrices
  • 4.4. Converses to Variation Diminution
  • Chapter 5. The Spectral Structure of TN Matrices
  • 5.0. Introduction
  • 5.1. Notation and Terms
  • 5.2. The Spectra of IITN Matrices
  • 5.3. Eigenvector Properties
  • 5.4. The Irreducible Case
  • 5.5. Other Spectral Results
  • Chapter 6. Determinantal Inequalities for TN Matrices
  • 6.0. Introduction
  • 6.1. Definitions and Notation
  • 6.2. Sylvester Implies Koteljanski?I
  • 6.3. Multiplicative Principal Minor Inequalities
  • 6.4. Some Non-principal Minor Inequalities
  • Chapter 7. Row and Column Inclusion and the Distribution of Rank
  • 7.0. Introduction
  • 7.1. Row and Column Inclusion Results for TN Matrices
  • 7.2. Shadows and the Extension of Rank Deficiency in Submatrices of TN Matrices
  • 7.3. The Contiguous Rank Property
  • Chapter 8. Hadamard Products and Powers of TN Matrices
  • 8.0. Definitions
  • 8.1. Conditions under which the Hadamard Product is TP/TN
  • 8.2. The Hadamard Core
  • 8.3. Oppenheim's Inequality
  • 8.4. Hadamard Powers of TP2
  • Chapter 9. Extensions and Completions
  • 9.0. Line Insertion
  • 9.1. Completions and Partial TN Matrices
  • 9.2. Chordal Case--MLBC Graphs
  • 9.3. TN Completions: Adjacent Edge Conditions
  • 9.4. TN Completions: Single Entry Case
  • 9.5. TN Perturbations: The Case of Retractions
  • Chapter 10. Other Related Topics on TN Matrices
  • 10.0. Introduction and Topics
  • 10.1. Powers and Roots of TP/TN Matrices
  • 10.2. Subdirect Sums of TN Matrices
  • 10.3. TP/TN Polynomial Matrices
  • 10.4. Perron Complements of TN Matrices
  • Bibliography
  • List of Symbols
  • Index

Similar Items