Hadamard Matrices Constructions using Number Theory and Linear Algebra
Hadamard Matrices Constructions using Number Theory and Linear Algebra by Jennifer Seberry is a comprehensive resource published by John Wiley & Sons on August 25, 2020. This 352-page book presents a detailed discussion of Hadamard matrices, covering both fundamental definitions and advanced topics, making it suitable for students and researchers alike.
Readers will find an exploration of various aspects of Hadamard matrices, including Gauss sums, Jacobi sums, and the properties of symmetric and skew Hadamard matrices. The text also delves into applications relevant to mathematics and number theory, providing insights into concepts such as Galois rings and Paley difference sets. This edition serves as both a textbook for graduate courses in combinatorics and a reference for ongoing research in the field, highlighting the practical relevance of Hadamard matrices in areas like signal processing and experimental design.
Official synopsis Publisher
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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