Book contents
- Frontmatter
- Dedication
- Contents
- Foreword
- Preface
- Part One Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension
- Part Two Entrywise Functions Preserving Positivity in all Dimensions
- Part Three Entrywise Polynomials Preserving Positivity in a Fixed Dimension
- 24 Entrywise Polynomial Preservers and Horn–Loewner-Type Conditions
- 25 Polynomial Preservers for Rank-1 Matrices, via Schur Polynomials
- 26 First-Order Approximation and the Leading Term of Schur Polynomials
- 27 Exact Quantitative Bound – Monotonicity of Schur Ratios
- 28 Polynomial Preservers on Matrices with Real or Complex Entries
- 29 Cauchy and Littlewood’s Definitions of Schur Polynomials
- 30 Exercises
- 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
29 - Cauchy and Littlewood’s Definitions of Schur Polynomials
from Part Three - Entrywise Polynomials Preserving Positivity in a Fixed Dimension
Book contents
- Frontmatter
- Dedication
- Contents
- Foreword
- Preface
- Part One Preliminaries: Entrywise Powers Preserving Positivity in a Fixed Dimension
- Part Two Entrywise Functions Preserving Positivity in all Dimensions
- Part Three Entrywise Polynomials Preserving Positivity in a Fixed Dimension
- 24 Entrywise Polynomial Preservers and Horn–Loewner-Type Conditions
- 25 Polynomial Preservers for Rank-1 Matrices, via Schur Polynomials
- 26 First-Order Approximation and the Leading Term of Schur Polynomials
- 27 Exact Quantitative Bound – Monotonicity of Schur Ratios
- 28 Polynomial Preservers on Matrices with Real or Complex Entries
- 29 Cauchy and Littlewood’s Definitions of Schur Polynomials
- 30 Exercises
- 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. 256 - 263Publisher: Cambridge University PressPrint publication year: 2022