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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.
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