A Comprehensive Study of k-Circulant Matrices Derived from Generalized Padovan Numbers

This paper presents a review of the k-circulant matrices and the generalized Padovan numbers, it further outlines the importance of these numbers and matrices with regard to matrices analysis and number theory. Considering the potential practical applications of k-circulant matrices in combination and numerical analysis, we derive explicit formulas for sum of entries, maximum column and row sum norms, Euclidean norm, spectral norm, eigenvalues and determinant of these matrices. Our research also shows the analytical relationships which exist between the usual structure of k-circulant matrices and generalized Padovan numbers that could be useful for the theoretical and practical researches.