What is the extension of Schimdt Decomposition, of a bipartite Quantum system to a Multipartite Quantum system

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Harm Derksen

The higher order singular value decomposition or multi-linear singular value decomposition can be thought of as a generalization of the Schmidt Decomposition.

See: Lieven De Lathauwer; Bart De Moor; Joos Vandewalle (April 2000). "A multilinear Singular Value Decomposition". SIAM Journal on Matrix Analysis. 21 (4): 1253–1278.