Book contents
- Frontmatter
- Dedication
- Contents
- Foreword
- Preface
- Part One Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension
- 1 The Cone of Positive Semidefinite Matrices
- 2 The Schur Product Theorem and Nonzero Lower Bounds
- 3 Totally Positive (TP) and Totally Nonnegative (TN) Matrices
- 4 Totally Positive Matrices – Generalized Vandermonde and Hankel Moment Matrices
- 5 Entrywise Powers Preserving Positivity in a Fixed Dimension
- 6 Midconvex Implies Continuity, and 2 × 2 Preservers
- 7 Entrywise Preservers of Positivity on Matrices with Zero Patterns
- 8 Entrywise Powers Preserving Positivity, Monotonicity, and Superadditivity
- 9 Loewner Convexity and Single Matrix Encoders of Preservers
- 10 Exercises
- Part Two Entrywise Functions Preserving Positivity in all Dimensions
- Part Three Entrywise Polynomials Preserving Positivity in a Fixed Dimension
- Part I: Bibliographic Notes and References
- Part II: Bibliographic Notes and References
- Part III: Bibliographic Notes and References
- References
- Index
This chapter is part of a book that is no longer available to purchase from Cambridge Core
6 - Midconvex Implies Continuity, and 2 × 2 Preservers
from Part One - Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension
Book contents
- Frontmatter
- Dedication
- Contents
- Foreword
- Preface
- Part One Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension
- 1 The Cone of Positive Semidefinite Matrices
- 2 The Schur Product Theorem and Nonzero Lower Bounds
- 3 Totally Positive (TP) and Totally Nonnegative (TN) Matrices
- 4 Totally Positive Matrices – Generalized Vandermonde and Hankel Moment Matrices
- 5 Entrywise Powers Preserving Positivity in a Fixed Dimension
- 6 Midconvex Implies Continuity, and 2 × 2 Preservers
- 7 Entrywise Preservers of Positivity on Matrices with Zero Patterns
- 8 Entrywise Powers Preserving Positivity, Monotonicity, and Superadditivity
- 9 Loewner Convexity and Single Matrix Encoders of Preservers
- 10 Exercises
- Part Two Entrywise Functions Preserving Positivity in all Dimensions
- Part Three Entrywise Polynomials Preserving Positivity in a Fixed Dimension
- Part I: Bibliographic Notes and References
- Part II: Bibliographic Notes and References
- Part III: Bibliographic Notes and References
- References
- Index
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- Matrix Analysis and Entrywise Positivity Preservers , pp. 46 - 54Publisher: Cambridge University PressPrint publication year: 2022