CRETAN (4t + 1) MATRICES (160,00 руб.)

Results: In the paper, we give an infinite number of new Cretan(4t + 1) matrices constructed by the use of regular Hadamard matrices, SBIBD(4t + 1; k; λ), weighing matrices, generalized Hadamard matrices and Kronecker product. <...> We introduce an inequality for the matrix radius and give a construction for a Cretan matrix of any order n ≥ 5. <...> Purpose: We tried to obtain a Cretan(4t + 1) matrix of order 4t + 1, i.e. an orthogonal matrix whose elements have Keywords — Hadamard Matrices, Regular Hadamard Matrices, OrthogonalMatrices, Symmetric Balanced Incomplete Block Designs (SBIBD), Cretan Matrices,Weighing Matrices, Generalized Hadamard Matrices, 05B20. <...> Introduction An application in image processing (compression, masking) led to the search for orthogonal matrices, all of whose elements have modulus 1 and which have maximal or high determinant. <...> Cretan matrices were first discussed, per se, during a conference in Crete in 2014. <...> This paper follows closely the joint work of N. A. Balonin, Jennifer Seberry and M. B. Sergeev [1–3]. <...> This present work emphasizes the 4t + 1 (Fermat type) orders with real elements 1. <...> Preliminary Definitions The absolute value of the determinant of any mafor the matrix of all 1’s and let  be a constant. <...> An orthogonal matrix, S, of order n, is square, has trix is not altered by 1) interchanging any two rows, 2) interchanging any two columns, and/or 3) multiplying any row/or column by –1. <...> These equivalence operations are called Hadamard equivalence operations. <...> So the absolute value of the determinant of any matrix is not altered by the use of Hadamard equivalence operation. <...> A Cretan matrix, S, of order n has entries with modulus 1 and at least one 1 per row and column. <...> It satisfies SST  In and so it is an orthogonal matrix. <...> A Cretan(n; ; ) matrix, or CM(n;; ) has  levels or values for its entries [1]. 2 ИНФОРМАЦИОННОУПРАВЛЯЮЩИЕ СИСТЕМЫ An Hadamard matrix of order n has entries ±1 and satisfies HHT  nIn for n  1, 2, 4t, t > 0 an integer. <...> Any Hadamard matrix can be put into normalized form, that is having the first row <...>