On the eigenstructures of functional K-potent matrices and their integral forms

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)244-253
Number of pages10
JournalWSEAS Transactions on Mathematics
Volume9
Issue number4
StatePublished - Apr 1 2010

Fingerprint

K-functional
Integral form
Cryptography
Idempotent Matrix
Image Encryption
Digital Image
Spectral Properties
Integral
Integer

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the eigenstructures of functional K-potent matrices and their integral forms. / Wu, Yan; Linder, Daniel F.

In: WSEAS Transactions on Mathematics, Vol. 9, No. 4, 01.04.2010, p. 244-253.

Research output: Contribution to journalArticle

@article{833e42abb1ae44299f7e0b92429930bb,
title = "On the eigenstructures of functional K-potent matrices and their integral forms",
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.",
keywords = "Diagonalizability, Idempotent, Image encryption, Involutary, Nilpotent, Skewed k-potent matrix, Unipotent",
author = "Yan Wu and Linder, {Daniel F}",
year = "2010",
month = "4",
day = "1",
language = "English (US)",
volume = "9",
pages = "244--253",
journal = "WSEAS Transactions on Mathematics",
issn = "1109-2769",
publisher = "World Scientific and Engineering Academy and Society",
number = "4",

}

TY - JOUR

T1 - On the eigenstructures of functional K-potent matrices and their integral forms

AU - Wu, Yan

AU - Linder, Daniel F

PY - 2010/4/1

Y1 - 2010/4/1

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 - http://www.scopus.com/inward/record.url?scp=77950218286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950218286&partnerID=8YFLogxK

M3 - Article

VL - 9

SP - 244

EP - 253

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

IS - 4

ER -