THE INTERCONNECTION OF ONE KIND OF QUASI-ORTHOGONAL MATRICES BUILT ON THE ORDERS OF THE SEQUENCES 4k AND 4k

The paper shows the interconnection among numbers, belonging to the sequences 4k and 4k – 1, and symmetric quasi-orthogonal matrices, ex-isting on orders equal to these numbers. To show the interconnection of such matrices through the simplest transformations. As a result, sequenc-es of natural numbers of the form 4k and 4k – 1 are considered, it is shown that the Mersenne matrices with rounded to integral values of the co-efficients are the «core» of the Hadamard matrices. The Hadamard matrices of different orders and types of symmetry of its «portraits» are of great practical importance for solving problems of information processing in medical diagnostic equipment, in tasks of videoinformation compression and transformation. The evaluation of Hadamard matrices through Mersenne matrices is simple, allowing one to quickly obtain a matrix, which is optimal for a particular issue.

Authors: A. M. Sergeev

Direction: Informatics and Computer Technologies

Keywords: Medical equipment, information processing, image transformation, numerical sequences, Mersenne numbers, quasi-orthogonal matrices, minimax matrices, Hadamard matrices, Mersenne matrices

View full article

THE INTERCONNECTION OF ONE KIND OF QUASI-ORTHOGONAL MATRICES BUILT ON THE ORDERS OF THE SEQUENCES 4k AND 4k – 1