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

Authors:
Yan Wu;Daniel F. Linder
Affiliations:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA;Department of Biostatistics, Medical College of Georgia, Augusta, GA
Venue:
WSEAS Transactions on Mathematics
Year:
2010

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Abstract

In this paper, a functional k-potent matrix satisfies the equation Ak = αI + βAr, 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.