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Hadamard matrices in $\{0,1\}$ presentation are square $m\times m$ matriceswhose entries are zeros and ones and whose rows considered as vectors in $\BbbR^m$ produce the Gram matrix of a special form with respect to the standardscalar product in $\Bbb R^m$. The concept of Hadamard matrices is extended inthe present paper. As a result pseudo-Hadamard matrices of the first generationare defined and investigated. An algorithm for generating these pseudo-Hadamardmatrices is designed and is used for testing some conjectures.

Pseudo-Hadamard matrices of the first generation and an algorithm for producing them