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.

Author Bio

Benjamin Lantz is currently pursuing an M.S. in Mathematics at Northern Arizona University. He recently obtained his BS in Mathematics and BS in Geography from Northern Arizona University in the spring. He plans to obtain a Ph.D. in Mathematics and eventually wants to become a mathematics professor.

Michael Zowada is currently pursuing a BS in Mathematics at Northern Arizona University. He plans on graduating in Spring 2013, pursuing his Ph.D. in Mathematics, and eventually becoming a mathematics professor.