  The matrix form of the presentation of the genetic code is described as the
cognitive form to analyze structures of the genetic code. A similar matrix form
is utilized in the theory of signal processing. The Kronecker family of the
genetic matrices is investigated, which is based on the genetic matrix [C A; U
G], where C, A, U, G are the letters of the genetic alphabet. This matrix in
the third Kronecker power is the (8*8)-matrix, which contains 64 triplets.
Peculiarities of the degeneracy of the vertebrate mitochondria genetic code are
reflected in the symmetrical black-and-white mosaic of this genetic
(8*8)-matrix. This mosaic matrix is connected algorithmically with Hadamard
matrices unexpectedly, which are famous in the theory of signal processing,
spectral analysis, quantum mechanics and quantum computers. A special
decomposition of numeric genetic matrices reveals their close relations with a
family of 8-dimensional hypercomplex numbers (not Cayley's octonions). Some
hypothesis and thoughts are formulated on the basis of these phenomenological
facts.
