Orthogonalities, linear operators, and characterization of inner product spaces
Sign Up to like & getrecommendations! Published in 2017 at "Aequationes mathematicae"
DOI: 10.1007/s00010-017-0494-7
Abstract: It is proved that a normed space, whose dimension is at least three, admitting a nonzero linear operator reversing Birkhoff orthogonality is an inner product space, which releases the smoothness condition in one of J.… read more here.
Keywords: product spaces; product; inner product; orthogonalities linear ... See more keywords
A Note on the Paper “The Algebraic Structure of the Arbitrary-Order Cone”
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Optimization Theory and Applications"
DOI: 10.1007/s10957-017-1102-7
Abstract: In this short paper, we look into a conclusion drawn by Alzalg (J Optim Theory Appl 169:32–49, 2016). We think the conclusion drawn in the paper is incorrect by pointing out three things. First, we… read more here.
Keywords: order cone; paper; inner product; cone ... See more keywords
A critical case of Rallis inner product formula
Sign Up to like & getrecommendations! Published in 2017 at "Science China Mathematics"
DOI: 10.1007/s11425-015-0770-7
Abstract: Let π be a genuine cuspidal representation of the metaplectic group of rank n. We consider the theta lifts to the orthogonal group associated to a quadratic space of dimension 2n+1. We show a case… read more here.
Keywords: formula; rallis inner; inner product; case ... See more keywords
Operators on positive semidefinite inner product spaces
Sign Up to like & getrecommendations! Published in 2020 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2020.03.004
Abstract: Abstract Let U be a semiunitary space; i.e., a complex vector space with scalar product given by a positive semidefinite Hermitian form 〈 ⋅ , ⋅ 〉 . If a linear operator A : U… read more here.
Keywords: operators positive; product; inner product; semidefinite inner ... See more keywords
On tuples of commuting operators in positive semidefinite inner product spaces
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DOI: 10.1016/j.laa.2020.06.015
Abstract: Abstract This paper is concerned with the study of certain properties of operator tuples on a complex Hilbert space H when a semi-inner product induced by a positive operator A on H is considered. In… read more here.
Keywords: operators positive; inner product; tuples commuting; commuting operators ... See more keywords
Spectrum of large random inner-product kernel matrices generated from lp ellipsoids
Sign Up to like & getrecommendations! Published in 2019 at "Communications in Statistics - Theory and Methods"
DOI: 10.1080/03610926.2019.1604962
Abstract: Abstract In this note, we study the n × n random kernel matrix whose entry is of form for some real function f and the xi’s are i.i.d. random vectors generated from lp ellipsoid or its surface… read more here.
Keywords: random inner; inner product; spectrum large; kernel matrices ... See more keywords
Manifestation of superposition and coherence in ${\mathcal P} {\mathcal T}$ -symmetry through the η-inner product
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/aaca46
Abstract: Through the $\eta$-inner product, we investigate $\cal PT$-symmetric quantum mechanics from the viewpoint of superposition and coherence theory. It is argued that $\cal PT$-symmetric quantum systems are endowed with stationary superposition or superposition-free properties. A… read more here.
Keywords: superposition coherence; cal symmetric; inner product; superposition ... See more keywords
Inner Product Regularized Nonnegative Self Representation for Image Classification and Clustering
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DOI: 10.1109/access.2017.2724763
Abstract: Feature selection, which aims to select the most informative feature subset, has been playing a critical role in dimension reduction. In this paper, a novel unsupervised feature selection algorithm called the inner product regularized nonnegative… read more here.
Keywords: image; algorithm; regularized nonnegative; product regularized ... See more keywords
Inner Product Computation In-Memory Using Distributed Arithmetic
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Circuits and Systems I: Regular Papers"
DOI: 10.1109/tcsi.2022.3193678
Abstract: In-memory computing using emerging technologies such as Resistive Random-Access Memory (ReRAM) has been proposed as a promising substitute for future computing applications to address the ‘von Neumann bottleneck’. Multiplication is the key component for inner… read more here.
Keywords: memory; memory using; inner product; product computation ... See more keywords
Privacy-Preserving Outsourced Inner Product Computation on Encrypted Database
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DOI: 10.1109/tdsc.2020.3001345
Abstract: We consider an outsourced computation model in the selective data sharing setting. Specifically, one of the data owners outsources the encrypted data to an untrusted cloud server, and wants to share the specific function of… read more here.
Keywords: computation; outsourced inner; inner product; product computation ... See more keywords
A Novel Deep Learning Network via Multiscale Inner Product With Locally Connected Feature Extraction for Intelligent Fault Detection
Sign Up to like & getrecommendations! Published in 2019 at "IEEE Transactions on Industrial Informatics"
DOI: 10.1109/tii.2019.2896665
Abstract: Intelligent fault detection is an important application of artificial intelligence and has been widely used in many mechanical systems. The shipborne antenna that is a typical and an important mechanical system plays an irreplaceable role… read more here.
Keywords: inner product; intelligent fault; fault detection; fault ... See more keywords