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2012•Rose-Hulman Scholar (Rose–Hulman Institute of Technology)Open access

An Overview of Complex Hadamard Cubes

Ben Lantz, Michael Zowada

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Abstract

Hadamard matrices have been studied by many authors, but higher-dimensional generalizations of Hadamard matrices are new and still relatively unexplored. This paper will present an overview of Hadamard matrices and their generalizations. In particular we will explore Walsh functions and Hadamard matrices. We will also extend Yang's Product Construction to create complex 3-D Hadamard cubes.

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What this paper is about

Hadamard matrices have been studied by many authors, but higher-dimensional generalizations of Hadamard matrices are new and still relatively unexplored. This paper will present an overview of Hadamard matrices and their generalizations. In particular we will explore Walsh functions and Hadamard matrices. We will also extend Yang's Product Construction to create complex 3-D Hadamard cubes.

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Available abstract

Hadamard matrices have been studied by many authors, but higher-dimensional generalizations of Hadamard matrices are new and still relatively unexplored. This paper will present an overview of Hadamard matrices and their generalizations. In particular we will explore Walsh functions and Hadamard matrices. We will also extend Yang's Product Construction to create complex 3-D Hadamard cubes.

Key concepts: Hadamard transform, Complex Hadamard matrix, Hadamard's inequality, Hadamard product, Hadamard matrix, Hadamard three-lines theorem, Hadamard's maximal determinant problem, Hadamard three-circle theorem

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