A Mathematical Proof of Double Helix DNA to Reverse Transcription RNA for Bioinformatics

  • Moon Ho Lee
  • Han HaiEmail author
  • Sung Kook Lee
  • Sergey V. Petoukhov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 658)


This paper presents a mathematical proof of deoxyribose nucleic acid (DNA) to ribonucleic acid (RNA) based on the block circulant Jacket matrix (BCJM) characteristics, which is used to develop a bioinformatics for the molecular communications. The DNA matrix decomposition is the form of the Kronecker product of identity and Hadamard matrices with pair complementarity. The RNA 4 by 4 genetic matrix is the anti-symmetric pair complementary of the core kernel. The variants of kernel of the Kronecker families are produced by permutations of the four letters C, A, U, G on positions in the matrix. Thus, we get 6 subset pattern of block circulant matrix, 6 upper-lower block symmetric matrix and 6 left-right block symmetric matrix. This decomposition of DNA to RNA leads very clearly to the Kronecker product of the symmetrical genetic matrices.


DNA double helix RNA Kronecker product identity & hadamard matrix symmetry complementary 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Moon Ho Lee
    • 1
  • Han Hai
    • 1
    Email author
  • Sung Kook Lee
    • 2
  • Sergey V. Petoukhov
    • 3
  1. 1.Division of Electronics and Information EngineeringChonbuk National UniversityJeonjuKorea
  2. 2.Dept. of EconomicsIndiana University-BloomingtonBloomingtonUSA
  3. 3.Institute of Machines StudiesRussian Academy of SciencesMoscowRussia

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