On the Existence, Method of Construction and Some Properties of (n - 2)-Structured Matrices Generating Bijective Transformations
( Pp. 93-105)

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Kononov Sergey A.
Secure Information Technology Assistance Foundation
Moscow, Russian Federation
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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.
How to Cite:
Kononov S.A., (2022), ON THE EXISTENCE, METHOD OF CONSTRUCTION AND SOME PROPERTIES OF (N - 2)-STRUCTURED MATRICES GENERATING BIJECTIVE TRANSFORMATIONS. Computational Nanotechnology, 1: 93-105. DOI: 10.33693/2313-223X-2022-9-1-93-105
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Keywords:
bijections, threshold functions, (n - 2)-structured matrices.