On two predictors of calculable chains of quasi-orthogonal matrices
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The general definition of quasi-orthogonal matrices, the definition of low-level matrices, and partial definitions of quasi-orthogonal Mersenne and Euler matrices are considered. New quasi-orthogonal symmetric Seidel matrices that exist on odd orders and three-level Legendre symbols used to calculate elements of these matrices are defined. A method to calculate Euler matrices via Mersenne matrices is given. A relation between asymmetric and symmetric odd-order Mersenne and Seidel matrices is shown to exist. A new, modified Sylvester method for calculating Euler matrices using symmetric circulant Seidel matrices is proposed.
Keywordsquasi-orthogonal matrices Hadamard matrices Belevitch matrices Mersenne matrices Euler matrices Seidel matrices three-level Legendre symbols two-circulant matrices
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