Mathematics – Numerical Analysis
Scientific paper
2010-05-11
Mathematics
Numerical Analysis
11 pages, 4 figures.
Scientific paper
Braman [B08] 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 transformations over vectors with real-valued scalars. This result is based upon a circulant-based tensor multiplication due to Kilmer et al. [KMP08]. 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 group to replace the cyclic group, any commutative ring with identity to replace the field of real numbers, and an arbitrary order tensor to replace third-order tensors, provided the underlying ring is commutative.
Navasca Carmeliza
Opperman Michael
Penderghest Timothy
Tamon Christino
No associations
LandOfFree
Tensors as module homomorphisms over group rings does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Tensors as module homomorphisms over group rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tensors as module homomorphisms over group rings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-385593