# The Lehmer matrix with recursive factorial entries

## Keywords:

Lehmer matrix, recursive coefficients, LU and Cholesky factorizations.## Abstract

A generalized Lehmer matrix with recursive entries from Kılıç et al. (2010b) is furthergeneralized, introducing three additional parameters and taking recursive factorials instead ofa term. Certain formulae are derived for the LU and Cholesky factorizations and their inverses,as well as the determinants. Then we precisely compute the elements of the inverse of thegeneralized Lehmer matrix.## References

Kılıç, E. 2010. The Generalized Fibonomial Matrix, European Journal of Combinatorics 31: 193-209.

Kılıç, E. & Prodinger, H. 2010a. A Generalized Filbert Matrix, The Fibonacci Quarterly 48(1): 29-33.

Kılıç, E. & Prodinger, H. 2013. Variants of the Filbert Matrix, The Fibonacci Quarterly 51(2): 153–162.

Kılıç, E. & Stanica, P. 2010b. The Lehmer matrix and its recursive analogue, Journal of Combinatrial Mathematics and Combinatorial Computing 74: 193-207.

Marcus, M. 1960. Basic theorems in matrix theory, National Bureau of Standards Applied Mathematics Series 57: 21–24.

Newman, M. & Todd, J. 1958. The evaluation of matrix inversion programs, Journal of the Society Industrial and Applied Mathematics 6: 466 - 476.

Stanica, P. 2005. Cholesky factorizations of matrices associated with r-order recurrent sequences, Integers: Electronic Journal of Combinatiorial Number Theory 5(2): #A16.