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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| Format: | Article |
| Language: | English |
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Elsevier
2021-12-01
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| Series: | Journal of King Saud University: Science |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1018364721002603 |
| 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. |
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| ISSN: | 1018-3647 |