### 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) |
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Pages (from-to) | 244-253 |

Number of pages | 10 |

Journal | WSEAS Transactions on Mathematics |

Volume | 9 |

Issue number | 4 |

State | Published - Apr 1 2010 |

### 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

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## Cite this

Wu, Y., & Linder, D. F. (2010). On the eigenstructures of functional K-potent matrices and their integral forms.

*WSEAS Transactions on Mathematics*,*9*(4), 244-253.