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Fuzzy Inner Product Space: Literature Review and a New Approach
Mathematics, 2021 The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature.
Lorena Popa, Lavinia Sida
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Inequalities That Imply the Norm of a Linear Space Is Induced by an Inner Product
Mathematics, 2023 The aim of this paper is to investigate when a linear normed space is an inner product space. Several conditions in a linear normed space are formulated with the help of inequalities. Some of them are from the literature and others are new. We prove that
Sorin Rădulescu +2 more
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Absence of Non-Trivial Fuzzy Inner Product Spaces and the Cauchy–Schwartz Inequality
Mathematics, 2020 First, we show that the non-trivial fuzzy inner product space under the linearity condition does not exist, which means a fuzzy inner product space with linearity produces only a crisp real number for each pair of vectors. If the positive-definiteness is
Taechang Byun +3 more
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On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space
Linear and Multilinear Algebra, 2004 Natalia Bebiano +2 more
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L$_p$-C$^*$-Semi-Inner Product Spaces [PDF]
Sahand Communications in Mathematical Analysis, 2022 This article introduces the notion of L$_p$-C$^*$-semi-inner product space, a generalization of the concept of C$^*$-semi-inner product space introduced by Gamchi et al., where we consider H\"{o}lder's inequality instead of Cauchy Schwartz' inequality ...
Zakiye Khalili +3 more
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Neutrosophic Real Inner Product Spaces [PDF]
Neutrosophic Sets and Systems, 2021 The objective of this work is to define for the first time the concept of inner product in a neutrosophic vector space and a refined neutrosophic vector space.
Mohammad Abobala
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VC dimension and inner product space induced by Bayesian networks
International Journal of Approximate Reasoning, 2009 Youlong Yang
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Cardinality Estimation in Inner Product Space
IEEE Open Journal of the Computer Society, 2022 This article addresses the problem of cardinality estimation in inner product spaces. Given a set of high-dimensional vectors, a query, and a threshold, this problem estimates the number of vectors such that their inner products with the query are not ...
Kohei Hirata +2 more
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Another Type of Fuzzy Inner Product Space
Iraqi Journal of Science, 2023 In this paper, we generalize the definition of fuzzy inner product space that is introduced by Lorena Popa and Lavinia Sida on a complex linear space. Certain properties of the generalized fuzzy inner product function are shown. Furthermore, we prove
Raghad I. Sabri, B. Ahmed
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Observing a changing Hilbert-space inner product
Physical Review Research, 2022 In quantum mechanics, physical states are represented by rays in Hilbert space H, which is a vector space imbued by an inner product 〈|〉, whose physical meaning arises as the overlap 〈ϕ|ψ〉 for |ψ〉 a pure state (description of preparation) and 〈ϕ| a ...
Salini Karuvade +2 more
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