• Corpus ID: 10106619

Tensors as module homomorphisms over group rings

  title={Tensors as module homomorphisms over group rings},
  author={Carmeliza Navasca and Michael Opperman and Tim Penderghest and Christino Tamon},
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… 

Figures from this paper

The power and Arnoldi methods in an algebra of circulants

The power and Arnoldi methods are derived in this algebra from inner products, norms, and other notions in the course of the derivation, which provides many generalizations of results from matrix or vector-space algebra.

Exact Tensor Completion Using t-SVD

By solving a convex optimization problem, which minimizes a conveX surrogate to the tubal-rank, one can guarantee exact recovery with high probability as long as number of samples is of the order, which is similar to the incoherence conditions for low-rank matrix completion under random sampling.

An algorithm for online tensor prediction

This work focuses on the specific case of 3-D tensors and exploits a recently developed framework of structured tensor decompositions to propose an online algorithm for learning and prediction of tensors with provable regret guarantees.

An Algorithm for Online Tensor Prediction: DRAFT Do Not Distribute

A recently developed framework of structured tensor decompositions is exploited to treat 3-D tensors as linear operators and appropriately generalize notions of rank and positive definiteness to tensors in a natural way.

WRC-19 Issues: Agenda Item 1.15 and the Use of 275-450 GHz

This column focuses on Agenda Item 1.15, identification of frequency bands for use by administrations for the land-mobile and fixed services applications operating in the frequency range 275-450 GHz, adopted at WRC-15.

An online tensor robust PCA algorithm for sequential 2D data

This paper proposes an online tensor robust PCA where the multidimensional data (tensor) is revealed sequentially in online mode, and tensor PCA is updated based on the latest estimation and the newly collected data.



A Third-order Generalization of the Matrix Svd as a Product of Third-order Tensors

This paper defines tensor-tensor multiplication in such a way so that it is closed under this operation, which results in new definitions for tensors such as the tensor transpose, inverse, and identity.

Matrices, 2nd edition, Chelsea

  • 1994

Tensor Decompositions Workshop Discussion Notes

  • American Institute of Mathematics, July 19-23, 2004.
  • 2004