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Statements

Subject Item
dbr:Matricization
dbo:wikiPageWikiLink
dbr:Tensor_reshaping
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dbr:Tensor_reshaping
Subject Item
dbr:Higher-order_singular_value_decomposition
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dbr:Tensor_reshaping
Subject Item
dbr:Multilinear_multiplication
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dbr:Tensor_reshaping
Subject Item
dbr:Tensor_reshaping
rdfs:label
Tensor reshaping
rdfs:comment
In multilinear algebra, a reshaping of tensors is any bijection between the set of indices of an order- tensor and the set of indices of an order- tensor, where . The use of indices presupposes tensors in coordinate representation with respect to a basis. The coordinate representation of a tensor can be regarded as a multi-dimensional array, and a bijection from one set of indices to another therefore amounts to a rearrangement of the array elements into an array of a different shape. Such a rearrangement constitutes a particular kind of linear map between the vector space of order- tensors and the vector space of order- tensors.
dcterms:subject
dbc:Tensors dbc:Multilinear_algebra
dbo:wikiPageID
18963290
dbo:wikiPageRevisionID
955671067
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dbr:Bijection dbr:Set_(mathematics) dbr:Canonical_isomorphism dbr:Standard_basis dbr:Field_(mathematics) dbr:Tensor_product dbr:Indexed_family dbr:Linear_map dbr:Permutation dbr:GNU_Octave dbr:Dimension_(vector_space) dbr:Vectorization_(mathematics) dbr:Tensor_order dbr:Multilinear_algebra dbr:Tensor_(intrinsic_definition) dbr:Vector_space dbr:Matlab dbc:Tensors dbc:Multilinear_algebra dbr:Coordinate_vector dbr:Basis_(linear_algebra) dbr:Function_(mathematics) dbr:Symmetric_group
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dbo:abstract
In multilinear algebra, a reshaping of tensors is any bijection between the set of indices of an order- tensor and the set of indices of an order- tensor, where . The use of indices presupposes tensors in coordinate representation with respect to a basis. The coordinate representation of a tensor can be regarded as a multi-dimensional array, and a bijection from one set of indices to another therefore amounts to a rearrangement of the array elements into an array of a different shape. Such a rearrangement constitutes a particular kind of linear map between the vector space of order- tensors and the vector space of order- tensors.
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wikipedia-en:Tensor_reshaping?oldid=955671067&ns=0
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Subject Item
dbr:Matricisation
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dbr:Tensor_reshaping
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dbr:Tensor_reshaping
Subject Item
wikipedia-en:Tensor_reshaping
foaf:primaryTopic
dbr:Tensor_reshaping