The Resource Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson
Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson
Resource Information
The item Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.
This item is available to borrow from 1 library branch.
- Summary
-
- "Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references"--
- ""Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems"--
- Language
- eng
- Extent
- 1 online resource (248 pages)
- Contents
-
- Totally Nonnegative Matrices; Contents; List of Figures; Preface; Chapter 0. Introduction; Chapter 1. Preliminary Results and Discussion; Chapter 2. Bidiagonal Factorization; Chapter 3. Recognition; Chapter 4. Sign Variation of Vectors and TN Linear Transformations; Chapter 5. The Spectral Structure of TN Matrices; Chapter 6. Determinantal Inequalities for TN Matrices; Chapter 7. Row and Column Inclusion and the Distribution of Rank; Chapter 8. Hadamard Products and Powers of TN Matrices; Chapter 9. Extensions and Completions; Chapter 10. Other Related Topics on TN Matrices; Bibliography
- Isbn
- 9781400839018
- Label
- Totally nonnegative matrices
- Title
- Totally nonnegative matrices
- Statement of responsibility
- Shaun M. Fallat, Charles R. Johnson
- Language
- eng
- Summary
-
- "Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references"--
- ""Totally Nonnegative Matrices" is a comprehensive, modern treatment of the titled class of matrices that arise in very many ways. Methodological background is given, and elementary bidiagonal factorization is a featured tool. In addition to historical highlights and sources of interest, some of the major topics include: recognition, variation diminution, spectral structure, determinantal inequalities, Hadamard products, and completion problems"--
- Assigning source
-
- Provided by publisher
- Provided by publisher
- Cataloging source
- N$T
- http://library.link/vocab/creatorName
- Fallat, Shaun M
- Dewey number
- 512.9/434
- Illustrations
- illustrations
- Index
- index present
- Language note
- In English
- LC call number
- QA188
- LC item number
- .F35 2011eb
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- http://library.link/vocab/relatedWorkOrContributorName
- Johnson, Charles R
- Series statement
- Princeton series in applied mathematics
- http://library.link/vocab/subjectName
-
- Non-negative matrices
- MATHEMATICS
- MATHEMATICS
- MATHEMATICS
- Non-negative matrices
- Label
- Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references (pages 219-238) and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- mixed
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- Totally Nonnegative Matrices; Contents; List of Figures; Preface; Chapter 0. Introduction; Chapter 1. Preliminary Results and Discussion; Chapter 2. Bidiagonal Factorization; Chapter 3. Recognition; Chapter 4. Sign Variation of Vectors and TN Linear Transformations; Chapter 5. The Spectral Structure of TN Matrices; Chapter 6. Determinantal Inequalities for TN Matrices; Chapter 7. Row and Column Inclusion and the Distribution of Rank; Chapter 8. Hadamard Products and Powers of TN Matrices; Chapter 9. Extensions and Completions; Chapter 10. Other Related Topics on TN Matrices; Bibliography
- Control code
- 713259161
- Dimensions
- unknown
- Extent
- 1 online resource (248 pages)
- File format
- unknown
- Form of item
- online
- Isbn
- 9781400839018
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1515/9781400839018
- Other physical details
- illustrations
- http://library.link/vocab/ext/overdrive/overdriveId
-
- 22573/ctt103qx
- cl0500000122
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
- (OCoLC)713259161
- Label
- Totally nonnegative matrices, Shaun M. Fallat, Charles R. Johnson
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references (pages 219-238) and index
- Carrier category
- online resource
- Carrier category code
-
- cr
- Carrier MARC source
- rdacarrier
- Color
- mixed
- Content category
- text
- Content type code
-
- txt
- Content type MARC source
- rdacontent
- Contents
- Totally Nonnegative Matrices; Contents; List of Figures; Preface; Chapter 0. Introduction; Chapter 1. Preliminary Results and Discussion; Chapter 2. Bidiagonal Factorization; Chapter 3. Recognition; Chapter 4. Sign Variation of Vectors and TN Linear Transformations; Chapter 5. The Spectral Structure of TN Matrices; Chapter 6. Determinantal Inequalities for TN Matrices; Chapter 7. Row and Column Inclusion and the Distribution of Rank; Chapter 8. Hadamard Products and Powers of TN Matrices; Chapter 9. Extensions and Completions; Chapter 10. Other Related Topics on TN Matrices; Bibliography
- Control code
- 713259161
- Dimensions
- unknown
- Extent
- 1 online resource (248 pages)
- File format
- unknown
- Form of item
- online
- Isbn
- 9781400839018
- Level of compression
- unknown
- Media category
- computer
- Media MARC source
- rdamedia
- Media type code
-
- c
- Other control number
- 10.1515/9781400839018
- Other physical details
- illustrations
- http://library.link/vocab/ext/overdrive/overdriveId
-
- 22573/ctt103qx
- cl0500000122
- Quality assurance targets
- not applicable
- Reformatting quality
- unknown
- Sound
- unknown sound
- Specific material designation
- remote
- System control number
- (OCoLC)713259161
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