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...

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Autor principal:	Muneerah Al Nuwairan
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Inner product Norm Parallelogram identity Parallelepiped law Binomial coefficient Science (General) Q1-390
Acceso en línea:	https://doaj.org/article/883924151a854d3cad31bce153e0f5d1
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spelling	oai:doaj.org-article:883924151a854d3cad31bce153e0f5d12021-11-18T04:43:54ZAn algorithm for verifying some norm identities in inner-product spaces1018-364710.1016/j.jksus.2021.101598https://doaj.org/article/883924151a854d3cad31bce153e0f5d12021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S1018364721002603https://doaj.org/toc/1018-3647In 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.Muneerah Al NuwairanElsevierarticleInner productNormParallelogram identityParallelepiped lawBinomial coefficientScience (General)Q1-390ENJournal of King Saud University: Science, Vol 33, Iss 8, Pp 101598- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Inner product Norm Parallelogram identity Parallelepiped law Binomial coefficient Science (General) Q1-390
spellingShingle	Inner product Norm Parallelogram identity Parallelepiped law Binomial coefficient Science (General) Q1-390 Muneerah Al Nuwairan An algorithm for verifying some norm identities in inner-product spaces
description	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.
format	article
author	Muneerah Al Nuwairan
author_facet	Muneerah Al Nuwairan
author_sort	Muneerah Al Nuwairan
title	An algorithm for verifying some norm identities in inner-product spaces
title_short	An algorithm for verifying some norm identities in inner-product spaces
title_full	An algorithm for verifying some norm identities in inner-product spaces
title_fullStr	An algorithm for verifying some norm identities in inner-product spaces
title_full_unstemmed	An algorithm for verifying some norm identities in inner-product spaces
title_sort	algorithm for verifying some norm identities in inner-product spaces
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/883924151a854d3cad31bce153e0f5d1
work_keys_str_mv	AT muneerahalnuwairan analgorithmforverifyingsomenormidentitiesininnerproductspaces AT muneerahalnuwairan algorithmforverifyingsomenormidentitiesininnerproductspaces
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An algorithm for verifying some norm identities in inner-product spaces

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