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{{Short description|Any scheme for expressing a tensor as a sequence of elementary operations acting on other, often simpler tensors}}
{{Unreferenced|date=January 2018}}
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 decomposition]]s.<ref>{{Cite journal|date=2013-05-01|title=General tensor decomposition, moment matrices and applications|url=https://www.sciencedirect.com/science/article/pii/S0747717112001290|journal=Journal of Symbolic Computation|language=en|volume=52|pages=51–71|doi=10.1016/j.jsc.2012.05.012|issn=0747-7171}}</ref>
The main tensor decompositions are:
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