Affiliation:
1. Department of Mathematics, TOBB Economics and Technology University , , Ankara , TURKEY
Abstract
ABSTRACT
We define a new matrix whose entries are defined by the idea of combining two different asymmetric rules. We will derive explicit formulæ for the matrices L and U come from LU-decomposition, L
−1, U
−1, inverse of the main matrix as well as its determinant. To prove the claimed results, we use backward induction method.
Reference12 articles.
1. Anderson, J. E.—Berg, C.: Quantum Hilbert matrices and orthogonal polynomials, J. Comput. Appl. Math. 223(3) (2009), 723–729.
2. Arikan, T.—Kiliç, E.—Prodinger, H.: A nonsymmetrical matrix and its factorizations, Math. Slovaca 69(4) (2019), 753–762.
3. Bozdağ, H.—Kiliç, E.—Akkus, I.: New Filbert and Lilbert matrices with asymmetric entries, Math. Slovaca 70(2) (2020), 289–296.
4. Carlitz, L.: The characteristic polynomial of a certain matrix of binomial coefficients, Fibonacci Quart. 3 (1965), 81–89.
5. Chu, W.—Claudio, L.: Binomial determinant evaluations, Ann. Comb. 9(4) (2005), 363–377.