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A Generalized Spectral Theory for Tensors Technical Report

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English
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technical report
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application/pdf
Extent
15 p.
Note (type = special display note)
Technical report DCS-TR-663
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School of Arts and Sciences (SAS) (New Brunswick)
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Computer Science (New Brunswick)
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Text
TitleInfo
Title
A Generalized Spectral Theory for Tensors Technical Report
Abstract (type = abstract)
In this paper we proposes a generalized spectral theory for tensors. Our proposed factorization decomposes a symmetric tensor into a product of an orthogonal and a diagonal tensor. In the same time, our factorization offers an expansion of a tensor as a summation of lower rank tensors that are obtained through an outer product defined on matrices. Our proposed factorization shows the relationship between the eigen-objects (eigen matrices and eigen vectors for order 3 tensor) and the generalized determinant and trace operators. Our framework is based on a consistent multilinear algebra that explains how we can generalize the notion of Hermitian matrices, the notion of transpose, and most importantly the notion of orthogonality for tensors.
Name (type = personal)
NamePart (type = family)
Gnang
NamePart (type = given)
Edinah K.
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Elgammal
NamePart (type = given)
Ahmed
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Retakh
NamePart (type = given)
Vladimir
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (authority = marcrt); (type = text)
author
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = yes); (qualifier = exact)
2010-02
RelatedItem (type = host)
TitleInfo
Title
Elgammal, Ahmed
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rucore30188000001
RelatedItem (type = host)
TitleInfo
Title
Computer Science (New Brunswick)
Identifier (type = local)
rucore21032500001
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3QC06ZF
Genre (authority = ExL-Esploro)
Technical Documentation
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Status
Open
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Technical

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Document
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1.3
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Mac OS X 10.5.8 Quartz PDFContext
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2010-02-04T19:19:10
DateCreated (point = end); (encoding = w3cdtf); (qualifier = exact)
2010-02-04T19:19:10
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