Determinant Optimization Method

  • Nikolay A. BaloninEmail author
  • Mikhail B. Sergeev
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 902)


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.


Hadamard matrices Determinant Determinant maximum D-matrices Quasi-orthogonal matrices Cretan matrices C-matrices Cyclic matrices 



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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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Saint Petersburg State University of Aerospace InstrumentationSt. PetersburgRussian Federation

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