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Determinant Optimization Method

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Advances in Artificial Systems for Medicine and Education II (AIMEE2018 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 902))

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Abstract

This article is devoted to matrices which play a significant role in digital signal processing, artificial intelligence systems, and mathematical natural sciences in the whole. The study of the world of matrices is going on intensively all over the world and constantly brings useful and unexpected results. This paper discusses the determinant optimization method for finding so-called quasi-orthogonal matrices. It is shown that the area of its application is extended due to matching of quasi-orthogonal matrices, which are locally optimal by their determinants (Cretan matrices), and non-orthogonal matrices of determinant maximum (D-matrices). All necessary definitions of matrices and their properties, used in the optimization algorithm, are provided. Two realizations of the algorithm are given—the basic and the reversed one. Examples of matrices calculated using the proposed method are given.

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Acknowledgements

The authors wish to sincerely thank Tamara Balonina for converting this paper into printing format. The authors also would like to acknowledge the great help of Professor Jennifer Seberry. The research leading to these results has received funding from the Ministry of Education and Science of the Russian Federation according to the project part of the state funding assignment 2.2200.2017/4.6.

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Authors and Affiliations

  1. Saint Petersburg State University of Aerospace Instrumentation, 67, B. Morskaia St., 190000, St. Petersburg, Russian Federation

    Nikolay A. Balonin & Mikhail B. Sergeev

Authors
  1. Nikolay A. Balonin
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  2. Mikhail B. Sergeev
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Corresponding author

Correspondence to Nikolay A. Balonin .

Editor information

Editors and Affiliations

  1. School of Educational Information Technology, Central China Normal University, Wuhan, Hubei, China

    Zhengbing Hu

  2. Mechanical Engineering Research Institute, Russian Academy of Sciences, Moscow, Russia

    Sergey V. Petoukhov

  3. Halmos College of Natural Sciences and Oceanography, Nova Southeastern University, Davie, FL, USA

    Matthew He

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Balonin, N.A., Sergeev, M.B. (2020). Determinant Optimization Method. In: Hu, Z., Petoukhov, S., He, M. (eds) Advances in Artificial Systems for Medicine and Education II. AIMEE2018 2018. Advances in Intelligent Systems and Computing, vol 902. Springer, Cham. https://doi.org/10.1007/978-3-030-12082-5_14

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