Tensor decomposition

In multilinear algebra, a tensor decomposition is any scheme for expressing a tensor as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions.

The main tensor decompositions are:

• tensor rank decomposition;
• higher-order singular value decomposition;
• Tucker decomposition;
• matrix product states, or tensor trains;
• hierarchical Tucker decomposition; and
• block term decomposition.