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 .
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.
In this paper, we give another proofs of two well-known results relative to the Jacobsthal and Jacobsthal-Lucas sequences and revise one of them. Moreover, we establish two equalities between this two sequences and referred closed-form sequences.
factorizations of Toeplitz matrices for some small sizes. Furthermore, we obtain the inverse of referred Toeplitz matrices by appling the above-mentioned results.
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.