The Kronecker tensor product of matrices is one of the most important operations in quantum mechanics and quantum informatics. The article is devoted to various applications of this mathematical operation for revealing hidden interrelations among molecular-genetic structures and for developing quantum biology and algebraic biology. Special attention is paid to matrix representations of the set of DNA nucleobases and their hydrogen bonds. These representations reveal, in particular, hidden symmetries in alphabets of DNA n-plets and also possibilities of applications of hyperbolic numbers and their extensions for modeling some hidden regularities in long DNA sequences.