Research Article
Year 2016,
Volume: 29 Issue: 3, 675 - 679, 30.09.2016
Abstract
References
- M. Aigner, Combinatorial Theory, Springer-Verlag, 1979.
- I. Akkuş, The Lehmer matrix with recursive factorial entries, Kuwait J. Sci, 42 (2015), no. 2, 34–41.
- B.V.R. Bhat, On greatest common divisor matrices and their applications, Linear Algebra Appl. 158 (1991) 77-97.
- R. Bhatia, Min matrices and Mean matrices, Math. Intelligencer 33, no.2 (2011) 22-28.
- E. Kılıç, P. Stanica, The Lehmer matrix and its recursive analogue, J. Combinat. Math and Combinat. Computing 74 (2010) 193-207.
- I. Korkee, P. Haukkanen, On meet and join matrices associated with incidence functions, Linear Algebra Appl. 372 (2003) 127-153.
- D. H. Lehmer, Problem E710, Amer. Math. Monthly, 53 (1946) p.97.
- M. Marcus, Basic Theorems in Matrix Theory, Nat. Bur. Standarts Appl. Math. Ser 57 (1960) 21-24.
- M. Mattila, On the eigenvalues of combined meet and join matrices, Linear Algebra Appl. 466 (2015) 1-20.
- M. Mattila, P. Haukkanen, Studying the various properties of MIN AND MAX matrices –elementary vs. more advanced methods, Spec. Matrices 4 (2016), Art. 10.
- M. Newman, J. Todd, The evaluation of matrix inversion programs, J. Society Industrial and Appl. Math. 6 (1958) 466-476.
- L. F. Shampine, The condition of certain matrices, J Res. Natl. Inst. Stan. B Mathematics and Mathematical Physics 69B no.4 (1965) 333-334.
- D. M. Smiley and M. F. Smiley, and J. Williamson, Amer. Math. Monthly, 53 (1946) 534-535.
Year 2016,
Volume: 29 Issue: 3, 675 - 679, 30.09.2016
Abstract
In this paper, we present a lattice-theoretic generalization of the Lehmer matrix. We obtain some certain formulae for the determinant and the entries of the inverse of this new generalization by using lattice-theoretic tools. These formulae are generalization of formulae for the determinant and the inverse of the classical Lehmer matrix and most of its generalizations presented in the literature.
References
- M. Aigner, Combinatorial Theory, Springer-Verlag, 1979.
- I. Akkuş, The Lehmer matrix with recursive factorial entries, Kuwait J. Sci, 42 (2015), no. 2, 34–41.
- B.V.R. Bhat, On greatest common divisor matrices and their applications, Linear Algebra Appl. 158 (1991) 77-97.
- R. Bhatia, Min matrices and Mean matrices, Math. Intelligencer 33, no.2 (2011) 22-28.
- E. Kılıç, P. Stanica, The Lehmer matrix and its recursive analogue, J. Combinat. Math and Combinat. Computing 74 (2010) 193-207.
- I. Korkee, P. Haukkanen, On meet and join matrices associated with incidence functions, Linear Algebra Appl. 372 (2003) 127-153.
- D. H. Lehmer, Problem E710, Amer. Math. Monthly, 53 (1946) p.97.
- M. Marcus, Basic Theorems in Matrix Theory, Nat. Bur. Standarts Appl. Math. Ser 57 (1960) 21-24.
- M. Mattila, On the eigenvalues of combined meet and join matrices, Linear Algebra Appl. 466 (2015) 1-20.
- M. Mattila, P. Haukkanen, Studying the various properties of MIN AND MAX matrices –elementary vs. more advanced methods, Spec. Matrices 4 (2016), Art. 10.
- M. Newman, J. Todd, The evaluation of matrix inversion programs, J. Society Industrial and Appl. Math. 6 (1958) 466-476.
- L. F. Shampine, The condition of certain matrices, J Res. Natl. Inst. Stan. B Mathematics and Mathematical Physics 69B no.4 (1965) 333-334.
- D. M. Smiley and M. F. Smiley, and J. Williamson, Amer. Math. Monthly, 53 (1946) 534-535.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | September 30, 2016 |
| Published in Issue | Year 2016 Volume: 29 Issue: 3 |