On the Existence, Method of Construction and Some Properties of (n - 2)-Structured Matrices Generating Bijective Transformations
- Authors: Kononov S.A.1
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Affiliations:
- Secure Information Technology Assistance Foundation
- Issue: Vol 9, No 1 (2022)
- Pages: 93-105
- Section: Articles
- URL: https://journals.eco-vector.com/2313-223X/article/view/529864
- DOI: https://doi.org/10.33693/2313-223X-2022-9-1-93-105
- ID: 529864
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Abstract
The article considers a new type of matrices that define bijective coordinate-threshold mappings - (n - 2)- structured matrices. It is proved that different matrices define different transformations, all (n - 2)-structured matrices of order 4 are described. For an arbitrary n ∈ ℕ, n classes of (n - 2)-structured matrices are specified, it is proved that the transformations specified by these matrices generate the group S2 S2n - 1. It is shown that the matrix transposed to the given one generates the inverse transformation.
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About the authors
Sergey A. Kononov
Secure Information Technology Assistance Foundation
Email: cononovsa@yandex.ru
Moscow, Russian Federation
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