Lower Bounds of Inner Products

Abstract

In this paper, we shall discuss the lower bounds for real positive difinite inner products in vector spaces V or R. The inner product of two vectors v and w in Vis denoted by <v,w>. The upper bound of this inner product is given by the famous Schwarz inequality which reads |<v,w>|≦||v|| ||w|| for all v, w in V. Here, we intend to reverse the Schwarz inequality. Consequently,we have a lower bound of this inner product which gives a useful application to the approximation of the evaluation of integrations.