Hadamar matrices. Patterns of construction, properties, applications. Monograph

Adamara matrices (H -matrixes) are an important tool for encoding and transmitting information. These matrices became known in 1893, when Jacques Adamar published his theory of inequalities and matrices. The Adamara matrix is ​​the square matrix of order N, consisting of numbers 1 and -1, the lines of which are pairing in pairs. The hypothesis of Adamar is widely known, according to which for all numbers M, multiple of 4, there are matrices of Adamar Mr. M. This hypothesis, also known as the problem of Adamar, has not yet been proven. Many scientists tried to solve this problem. On this topic, a large number of works were written. The most famous of the authors of these works are Hall, Hedayyat, Wallis, Harmouth, Djokovic, Bomer, Elikh. Among domestic scientists, Yablonsky, Lupanov, Arshinov, Sadovsky, Litvin, etc. can be distinguished. The result of the work of these scientists was a number of proven statements about the existence of matrices of Adamar of the given orders. The purpose of this work is to find patterns in the application of these statements