On the movements induced by the iterative product of 2 × 2 matrices defined in modulo 7

Seunghoon Jung; Jae Sung Moon; Daeyeoul Kim

On the movements induced by the iterative product of 2 × 2 matrices defined in modulo 7

Seunghoon Jung
, Jae Sung Moon
, Daeyeoul Kim^*

^*Corresponding author for this work

Department of Mathematics

Jeonbuk National University

Research output: Contribution to journal › Journal article › peer-review

Abstract

We observe the sequence of matrices obtained by repeated iterations of the 2×2 matrix in modulo 7, define them as stable, amicable, and sociable, understand their various properties, and give some results about their behavior. Also we will define 0, 1, 2, 3, 4, 5, 6 as the movement of a point up, down, left, right, and diagonally in real plane or spaces. Finally, we want to investigate patterns in the behavior of the matrix sequence.

Original language	English
Article number	MTJPAM-D-25-00028
Pages (from-to)	16-32
Number of pages	17
Journal	Montes Taurus Journal of Pure and Applied Mathematics
Volume	7
Issue number	3
State	Published - 2025

Keywords

amicable pair
Iteration
matrices
movements
sociable

Cite this

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title = "On the movements induced by the iterative product of 2 × 2 matrices defined in modulo 7",

abstract = "We observe the sequence of matrices obtained by repeated iterations of the 2×2 matrix in modulo 7, define them as stable, amicable, and sociable, understand their various properties, and give some results about their behavior. Also we will define 0, 1, 2, 3, 4, 5, 6 as the movement of a point up, down, left, right, and diagonally in real plane or spaces. Finally, we want to investigate patterns in the behavior of the matrix sequence.",

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AU - Jung, Seunghoon

AU - Moon, Jae Sung

AU - Kim, Daeyeoul

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N2 - We observe the sequence of matrices obtained by repeated iterations of the 2×2 matrix in modulo 7, define them as stable, amicable, and sociable, understand their various properties, and give some results about their behavior. Also we will define 0, 1, 2, 3, 4, 5, 6 as the movement of a point up, down, left, right, and diagonally in real plane or spaces. Finally, we want to investigate patterns in the behavior of the matrix sequence.

AB - We observe the sequence of matrices obtained by repeated iterations of the 2×2 matrix in modulo 7, define them as stable, amicable, and sociable, understand their various properties, and give some results about their behavior. Also we will define 0, 1, 2, 3, 4, 5, 6 as the movement of a point up, down, left, right, and diagonally in real plane or spaces. Finally, we want to investigate patterns in the behavior of the matrix sequence.

KW - amicable pair

KW - Iteration

KW - matrices

KW - movements

KW - sociable

UR - https://www.scopus.com/pages/publications/105012031215

M3 - Journal article

AN - SCOPUS:105012031215

SN - 2687-4814

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JO - Montes Taurus Journal of Pure and Applied Mathematics

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IS - 3

M1 - MTJPAM-D-25-00028

ER -

On the movements induced by the iterative product of 2 × 2 matrices defined in modulo 7

Abstract

Keywords

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