On the Eigenstructures of Functional K-Potent Matrices and Their Integral Forms

Yan Wu; Daniel F. Linder

On the Eigenstructures of Functional K-Potent Matrices and Their Integral Forms

Yan Wu
, Daniel F. Linder

Mathematical Sciences

Augusta University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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Abstract

In this paper, a functional k-potent matrix satisfies the equation A ^k=αI +βA ^r, where k and r are positive integers, α and β are real numbers. This class of matrices includes idempotent, Nilpotent, and involutary matrices, and more. It turns out that the matrices in this group are best distinguished by their associated eigen-structures. The spectral properties of the matrices are exploited to construct integral k-potent matrices, which have special roles in digital image encryption.

Original language	American English
Journal	WSEAS Transactions on Mathematics
Volume	9
State	Published - Jan 1 2010

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Disciplines

Public Health
Biostatistics
Community Health

Keywords

Diagonalizability
Idempotent
Image encryption
Involutary
Nilpotent
Skewed k-potent matrix
Unipotent

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Cite this

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abstract = "In this paper, a functional k-potent matrix satisfies the equation A k=αI +βA r, where k and r are positive integers, α and β are real numbers. This class of matrices includes idempotent, Nilpotent, and involutary matrices, and more. It turns out that the matrices in this group are best distinguished by their associated eigen-structures. The spectral properties of the matrices are exploited to construct integral k-potent matrices, which have special roles in digital image encryption.",

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N2 - In this paper, a functional k-potent matrix satisfies the equation A k=αI +βA r, where k and r are positive integers, α and β are real numbers. This class of matrices includes idempotent, Nilpotent, and involutary matrices, and more. It turns out that the matrices in this group are best distinguished by their associated eigen-structures. The spectral properties of the matrices are exploited to construct integral k-potent matrices, which have special roles in digital image encryption.

AB - In this paper, a functional k-potent matrix satisfies the equation A k=αI +βA r, where k and r are positive integers, α and β are real numbers. This class of matrices includes idempotent, Nilpotent, and involutary matrices, and more. It turns out that the matrices in this group are best distinguished by their associated eigen-structures. The spectral properties of the matrices are exploited to construct integral k-potent matrices, which have special roles in digital image encryption.

KW - Diagonalizability

KW - Idempotent

KW - Image encryption

KW - Involutary

KW - Nilpotent

KW - Skewed k-potent matrix

KW - Unipotent

UR - https://digitalcommons.georgiasouthern.edu/biostat-facpubs/2

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JO - WSEAS Transactions on Mathematics

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ER -

On the Eigenstructures of Functional K-Potent Matrices and Their Integral Forms

Abstract

UN SDGs

Disciplines

Keywords

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