8. Matrix Genetics, Hadamard Matrices, and Algebraic Biology

  1. Matthew He1 and
  2. Sergey Petoukhov2

Published Online: 12 OCT 2010

DOI: 10.1002/9780470904640.ch8

Mathematics of Bioinformatics: Theory, Practice, and Applications

Mathematics of Bioinformatics: Theory, Practice, and Applications

How to Cite

He, M. and Petoukhov, S. (2010) Matrix Genetics, Hadamard Matrices, and Algebraic Biology, in Mathematics of Bioinformatics: Theory, Practice, and Applications, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470904640.ch8

Author Information

  1. 1

    Nova Southeastern University, Fort Lauderdale, Florida, USA

  2. 2

    Russian Academy of Sciences, Moscow, Russia

Publication History

  1. Published Online: 12 OCT 2010
  2. Published Print: 17 DEC 2010

Book Series:

  1. Bioinformatics: Computational Techniques and Engineering

Book Series Editors:

  1. Yi Pan and
  2. Albert Y. Zomaya

ISBN Information

Print ISBN: 9780470404430

Online ISBN: 9780470904640

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Keywords:

  • algebraic biology;
  • genetic code;
  • Hadamard matrices;
  • matrix genetics

Summary

This chapter is devoted to matrix forms of presentations of the genetic code for algebraic analysis of a basic scheme of degeneracy of the genetic code. Similar matrix forms are utilized in the theory of signal processing and encoding. The Kronecker family of genetic matrices is investigated, which is based on the genetic matrix [C A; U G], where C, A, U, and G are the letters of the genetic alphabet. Furthermore, many types of cyclic permutations of genetic elements lead to reconstruction of initial Hadamard matrices into new Hadamard matrices unexpectedly. This demonstrates that matrix algebra is one of the promising instruments and an adequate language in bioinformatics and algebraic biology. This chapter gives an example of one of the results that has already been arrived at in the field of matrix genetics.

Controlled Vocabulary Terms

Hadamard matrices; matrix algebra