# Tensors as module homomorphisms over group rings

@article{Navasca2010TensorsAM, title={Tensors as module homomorphisms over group rings}, author={Carmeliza Navasca and Michael Opperman and Tim Penderghest and Christino Tamon}, journal={ArXiv}, year={2010}, volume={abs/1005.1894} }

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…

## 7 Citations

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