Tangboonduangjit A.Wanasawat S.Mahidol University2025-03-242025-03-242025-04-01ICIC Express Letters Vol.19 No.4 (2025) , 403-4101881803Xhttps://repository.li.mahidol.ac.th/handle/123456789/106798We establish that under certain conditions, the generating matrix for the generalized Fibonacci sequence of order k can be diagonalized by a Vandermonde matrix. The purpose of this work is to investigate the properties of the generating matrix for the generalized Fibonacci sequence of order k and to derive new results related to its diagonalizability and applications. The results include a closed-form expression for the matrix’s powers and the determinant of a related Toeplitz matrix.Computer ScienceEngineeringArticleSCOPUS10.24507/icicel.19.04.4032-s2.0-86000666089