An algorithm for verifying some norm identities in inner-product spaces

In this paper, we provide an algorithm for verifying the validity of identities of the form ∑A⊆n¯cA‖xA‖2=0, where xA=∑i∈Axi 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 th...

Full description

Saved in:
Bibliographic Details
Published inJournal of King Saud University. Science Vol. 33; no. 8; p. 101598
Main Author Al Nuwairan, Muneerah
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2021
Elsevier
Subjects
Binomial coefficient
Inner product
Norm
Parallelepiped law
Parallelogram identity
Inner product
Norm
Binomial coefficient
Parallelogram identity
WLOG
Parallelepiped law
Online AccessGet full text

Cover

More Information
Summary:In this paper, we provide an algorithm for verifying the validity of identities of the form ∑A⊆n¯cA‖xA‖2=0, where xA=∑i∈Axi 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 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.
ISSN:1018-3647
DOI:10.1016/j.jksus.2021.101598