This thesis is an extension (and generalization) of the work(s) done by Loewner in 1934 ([9],[10]) . We give elementary proofs of the fact that the Loewner matrices corresponding to the function on are positive semidefinite , conditionally negative definite , and conditionally positive definite , for r in , and respectively . We show that in contrast to the interval the Loewner matrices corresponding to an operator convex function on eed not be conditionally negative definite . In addition to the matrices the matrices too have been of interest . It was shown by Kwong [13] that for these matrices are p.s.d . Different proofs of this fact have been given in [5] ,[8] and in [4] it was shown that these matrices are not just p.s.d . they are infinitely divisible . in [9] we showed that for the matrices are c.n.d .