An Algorithm for Verifying Some Norm Identities in Inner-Product Spaces

2019/11/13 by Nuwairan, Muneerah Al
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1911.05297

Abstract

In this paper, we provide an algorithm for verifying the validity of identities of the form \undersetA⊆n∑c_A\Vert x_A\Vert ²=0, where x_A=\underseti∈ A∑x_i and n=\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 parallelopiped 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.

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