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• W2115657796 abstract "Braman [1] described a construction where third-order tensors are exactly the set of linear transformations acting on the set of matrices with vectors as scalars. This extends the familiar notion that matrices form the set of all linear transformati ons over vectors with real-valued scalars. This result is based upon a circulant-based tensor multiplication due to Kilmer et al. [4]. In this work, we generalize these observations further by viewing this construction in its natural framework of group rings. The circulant-based products arise as convolutions in these algebraic structures. Our generalization allows for any abelian grou p to replace the cyclic group, any commutative ring with identity to replace the field of real nu mbers, and an arbitrary order tensor to replace third-order tensors, provided the underlying ri ng is commutative." @default.
• W2115657796 created "2016-06-24" @default.
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• W2115657796 date "2010-05-11" @default.
• W2115657796 modified "2023-09-27" @default.
• W2115657796 title "Tensors as module homomorphisms over group rings" @default.
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• W2115657796 hasPublicationYear "2010" @default.
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