Abstract
In this paper, we provide an algorithm for verifying the validity of identities of the form Sigma C-A subset of(n) over bar(A)parallel to x(A)parallel to(2) = 0, where x(A) = Sigma(i is an element of A)x(i) and (n) over bar = {1, ... , n} in inner-product spaces. Such algorithm is used to verify the validity, in inner-product spaces, for a number of identities. These include a generalization of the parallelepiped law. We also show that such identities hold only in inner-product spaces. Thus, the algorithm can be used to deduce characterizations of inner-product spaces. (C) 2021 The Author. Published by Elsevier B.V. on behalf of King Saud University.