In this paper, we give a proof of the inverse of the generalized Pascal matrix by mathematical induction.
In this paper, we give a proof of a theorem about the generalized Pascal matrix by mathematical induction.
In this paper, we establish a different proof of the determinant related to one kind of generalized Fibonacci sequence.
In this paper, we modify the determinant of the companion matrix of order k and give an inductive proof of it. KEYWORDS: Generalized Fibonacci and Pell number; companion matrix of order k.
We consider the Toeplitz matrices and obtain their unique LU factor-izations. As by-products, we get an explicit formula for the determinant of a Toeplitz matrix and the application of inversion of Toeplitz matrices .
We consider a special class of the generalized Vandermonde matrices and obtain an LU factorization for its member by giving closed-form formulae of the entries of L and U. Moreover, we express the matrices L and U as products of 1-banded (bidiagonal) matrices. Our result is applied to give the closed-form formula of the inverse of the considered matrix.