Altınışık, E.Taşcı, D.2020-03-262020-03-262002Altınışık, E., Taşcı, D., (2002). On a Generalization of the Reciprocal Lcm Matrix. Communications Series A1: Mathematics and Statistics, 51(2), 37-46.1303-59912618-6470http://www.trdizin.gov.tr/publication/paper/detail/TXpFNE1qYzM=https://hdl.handle.net/20.500.12395/17718Let S = {x,,, be a set of distinct positive integers. The nxn matrix 1/[S]=(s), where s=1/[x,,x,], the reciprocal of the least common multiple of x, and x,, is called the reciprocal least common multiple (reciprocal LCM) matrix on S. In this paper, we present a generalization of the reciprocal LCM matrix on S, that is the matrix 1/[S'], the ij- entry of which is 1/[x,,x,], where r is a real number. We obtain a structure theorem for 1/[S] and the value of the determinant of 1/[S"]. We also prove that 1/[S'] is positive definite if r>0. Then we calculate the inverse of 1/[S'] on a factor closed set. Finally, we show that the matrix [S']=([x,,x,]) defined on S is the product of an integral matrix and the generalized reciprocal LCM matrix 1/[S'] = (1/[x,,x,]) if S is factor closed and r is a positive integer.eninfo:eu-repo/semantics/openAccessİstatistik ve OlasılıkMatematikThe GCD matrixthe LCM matrixthe reciprocal GCD matrixthe reciprocal LCM matrixEuler's totient functionJordan's totient functionfactor closed setOther5123746