Definition
Let be a list of positive integers. Then the matrix having the greatest common divisor as its entry is referred to as the GCD matrix on .The LCM matrixBourque–Ligh conjecture
conjectured that the LCM matrix on a GCD-closed setReferences
{{reflist, refs = {{cite journal , last1 = Bourque , first1 = K. , last2 = Ligh , first2 = S. , title = On GCD and LCM matrices , journal = Linear Algebra and Its Applications , year = 1992 , volume = 174 , pages = 65–74 , doi = 10.1016/0024-3795(92)90042-9 , doi-access = free {{cite journal , last1 = Haukkanen , first1 = P. , last2 = Wang , first2 = J. , last3 = Sillanpää , first3 = J. , title = On Smith's determinant , journal = Linear Algebra and Its Applications , year = 1997 , volume = 258 , pages = 251–269 , doi = 10.1016/S0024-3795(96)00192-9 , doi-access = free {{cite journal , last = Hong , first = S. , title = On the Bourque–Ligh conjecture of least common multiple matrices , journal = Journal of Algebra , year = 1999 , volume = 218 , pages = 216–228 , doi = 10.1006/jabr.1998.7844 , doi-access = free {{cite journal , last1 = Korkee , first1 = I. , last2 = Mattila , first2 = M. , last3 = Haukkanen , first3 = P. , title = A lattice-theoretic approach to the Bourque–Ligh conjecture , journal = Linear and Multilinear Algebra , year = 2019 , volume = 67 , issue = 12 , pages = 2471–2487 , doi = 10.1080/03081087.2018.1494695 , s2cid = 117112282 , url = https://trepo.tuni.fi/handle/10024/117430 {{cite journal , last = Smith , first = H. J. S. , title = On the value of a certain arithmetical determinant , journal = Proceedings of the London Mathematical Society , year = 1875 , volume = 1 , pages = 208–213 , doi = 10.1112/plms/s1-7.1.208, url = https://zenodo.org/record/1709912 Matrix theory Number theory