  The Kronecker family of the genetic matrices is investigated, which is based
on the genetic matrix [C T; A G], where C, T, A, G are the letters of the
genetic alphabet. The matrix [C T; A G] in the second Kronecker power is the
(4*4)-matrix of 16 duplets. The matrix [C T; A G] in the third Kronecker power
is the (8*8)-matrix of 64 triplets. It is significant that peculiarities of the
degeneracy of the genetic code are reflected in the symmetrical black-and-white
mosaic of these genetic matrices. The article represents interesting
mathematical properties of these mosaic matrices, which are connected with
positional permutations inside duplets and triplets; with projector operators;
with unitary matrices and cyclic groups, etc. Fractal genetic nets are proposed
as a new effective tool to study long nucleotide sequences. Some results about
revealing new symmetry principles of long nucleotide sequences are described.
