Wolfgang Hackbusch

On the Representation of (Anti-)Symetric Tensors

In various applications symmetric or antisymmetric tensors are of interest. While there are very efficient representation schemes for general tensors, tensor formats for (anti-)symmetric tensors are more involved. We discuss the indirect and direct use of the canonical format and study the properties of the hierarchical format (TT). The difficulty in constructing a suitable sequence of subspaces are the implicit relations. If the minimal subspaces are known these are the perfect choices. However, if one selects a smaller subspace it may happen that only the zero tensor can be represented. The existence of nontrivial (anti-)symmetric tensors can be characterised by an algebraic criterion.

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