On some properties of k-circulant matrices with the generalized Pell-Padovan numbers

In this paper, we investigate the properties of the $k$-circulant matrix generated by the generalized Pell--Padovan numbers. We derive explicit formulas for the sum of entries, the maximum column sum norm ($\Vert \cdot \Vert _{1}$), the maximum row sum norm ($\Vert \cdot \Vert_{\infty }$), the Frobenius (Euclidean) norm ($\Vert \cdot \Vert _{F}$), as well as the eigenvalues and determinant of this matrix. Furthermore, we establish upper and lower bounds for its spectral norm ($\Vert \cdot \Vert_{2}$), thereby providing a comprehensive analysis of the structural andspectral characteristics of the $k$-circulant matrix associated with thegeneralized Pell--Padovan sequence.