222x Filetype PDF File size 1.56 MB Source: framerc.missouri.edu
Hadamard Matrices: Truth & Hadamard Matrices: Consequences Raymond Nguyen Truth & Consequences Advisor: Peter Casazza The University of Missouri Math 8190 (Master’s Project) Raymond Nguyen Basic Theory of Hadamard Advisor: Peter Casazza Matrices The University of Missouri Hadamard Matrix Constructions Math 8190 (Master’s Project) Applications of Hadamard Matrices Spring 2020 1/55 Hadamard Outline Matrices: Truth & Consequences Raymond Nguyen Advisor: Peter Casazza The University of Missouri 1 Basic Theory of Hadamard Matrices Math 8190 (Master’s Project) Basic Theory of Hadamard 2 Hadamard Matrix Constructions Matrices Hadamard Matrix Constructions Applications of 3 Applications of Hadamard Matrices Hadamard Matrices 2/55 Hadamard Table of Contents Matrices: Truth & Consequences Raymond Nguyen Advisor: Peter 1 Basic Theory of Hadamard Matrices Casazza The University of Missouri Definition & Examples Math 8190 (Master’s Project) Properties Basic Theory of Hadamard Matrices Definition & Examples The Hadamard Conjecture Properties The Hadamard Conjecture Hadamard Matrix Constructions 2 Hadamard Matrix Constructions Applications of Hadamard Matrices 3 Applications of Hadamard Matrices 3/55 Hadamard What is a Hadamard Matrix? Matrices: Truth & Consequences Raymond Nguyen Advisor: Peter Definition (Hadamard Matrix) Casazza The University of A square matrix H of order n whose entries are +1 or −1 is called a Missouri Math 8190 Hadamard matrix of order n provided its rows are pairwise orthogonal – (Master’s Project) i.e., Basic Theory of T Hadamard HH =n·In: (1) Matrices Definition & Examples Properties The Hadamard Conjecture Note that (1) implies that H has an inverse 1HT. Consequently, its Hadamard Matrix columns are also pairwise orthogonal – i.e., n Constructions Applications of Hadamard HTH =n·I : (2) Matrices n 4/55
no reviews yet
Please Login to review.