Hadamard Matrices
eBook - PDF

Hadamard Matrices

Constructions using Number Theory and Linear Algebra

,
  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Hadamard Matrices

Constructions using Number Theory and Linear Algebra

,
Book details
Table of contents
Citations

About This Book

Up-to-date resource on Hadamard matrices

Hadamard Matrices: Constructions using Number Theory and Algebra provides students with a discussion of the basic definitions used for Hadamard Matrices as well as more advanced topics in the subject, including:

  • Gauss sums, Jacobi sums and relative Gauss sums
  • Cyclotomic numbers
  • Plug-in matrices, arrays, sequences and M-structure
  • Galois rings and Menon Hadamard differences sets
  • Paley difference sets and Paley type partial difference sets
  • Symmetric Hadamard matrices, skew Hadamard matrices and amicable Hadamard matrices
  • A discussion of asymptotic existence of Hadamard matrices
  • Maximal determinant matrices, embeddability of Hadamard matrices and growth problem for Hadamard matrices

The book can be used as a textbook for graduate courses in combinatorics, or as a reference for researchers studying Hadamard matrices.

Utilized in the fields of signal processing and design experiments, Hadamard matrices have been used for 150 years, and remain practical today. Hadamard Matrices combines a thorough discussion of the basic concepts underlying the subject matter with more advanced applications that will be of interest to experts in the area.

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Information

Publisher
Wiley
Year
2020
ISBN
9781119520276
Edition
1
Topic
Mathematics
Subtopic
Number Theory
Index
Mathematics

Table of contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Contents
  5. List of Tables
  6. List of Figures
  7. Preface
  8. Acknowledgments
  9. Acronyms
  10. Introduction
  11. Chapter 1 Basic Definitions
  12. Chapter 2 Gauss Sums, Jacobi Sums, and Relative Gauss Sums
  13. Chapter 3 Plug-In Matrices
  14. Chapter 4 Arrays: Matrices to Plug-Into
  15. Chapter 5 Sequences
  16. Chapter 6 M-structures
  17. Chapter 7 Menon Hadamard Difference Sets and Regular Hadamard Matrices
  18. Chapter 8 Paley Hadamard Difference Sets and Paley Type Partial Difference Sets
  19. Chapter 9 Skew Hadamard, Amicable, and Symmetric Matrices
  20. Chapter 10 Skew Hadamard Difference Sets
  21. Chapter 11 Asymptotic Existence of Hadamard Matrices
  22. Chapter 12 More on Maximal Determinant Matrices
  23. Appendix A Hadamard Matrices
  24. Appendix B List of sds from Cyclotomy
  25. Appendix C Further Research Questions
  26. References
  27. Index
  28. EULA