### 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 | English (US) |
---|---|

Pages (from-to) | 244-253 |

Number of pages | 10 |

Journal | WSEAS Transactions on Mathematics |

Volume | 9 |

Issue number | 4 |

State | Published - Apr 1 2010 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory
- Endocrinology, Diabetes and Metabolism
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Management Science and Operations Research
- Control and Optimization
- Computational Mathematics
- Applied Mathematics

### Cite this

*WSEAS Transactions on Mathematics*,

*9*(4), 244-253.

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

Research output: Contribution to journal › Article

*WSEAS Transactions on Mathematics*, vol. 9, no. 4, pp. 244-253.

}

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

AN - SCOPUS:77950218286

VL - 9

SP - 244

EP - 253

JO - WSEAS Transactions on Mathematics

JF - WSEAS Transactions on Mathematics

SN - 1109-2769

IS - 4

ER -