Abstract. The validity of Hadamard hypothesis about the existence of orthogonal matrices of the maximum determinant with elements –1 and +1 of all orders of 4t with t being a natural number, which are widely used in problems of information processing, transformation, and encoding, is discussed. The "problematic" orders of Hadamard matrices for calculation by known methods, which do not allow to practically confirm the proof of the hypothesis, are presented. Hadamard matrices and Mersenne matrices are considered as mathematical objects whose search is fundamentally different. The relationship of Mersenne matrices existing for all orders (4t–1) with Hadamard matrices is given, which proves the existence of these matrices for all orders of 4t.

Keywords: orthogonal transformations, interrelation of orthogonal matrices, Hadamard matrices, quasi-orthogonal matrices, Mersenne matrices, Hadamard hypothesis

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