Three-Level Cretan Matrices of Order 37

Аннотация

Purpose: This note discusses three-level orthogonal matrices which were first highlighted by J. J. Sylvester. Hadamard matrices, symmetric conference matrices, and weighing matrices are the best known of these matrices with entries from the unit disk. The goal of this note is to develop a theory of such matrices based on preliminary research results. Methods: Extreme solutions (using the determinant) have been established by minimization of the maximum of the absolute values of the elements of the matrices followed by their subsequent classification. Results: We give a three-level Cretan(37). This is new and the first time such a matrix has been found whose order is other than a 2