In multilinear algebra, the tensor rank decomposition or canonical polyadic decomposition (CPD) may be regarded as a generalization of the matrix singular value decomposition (SVD) to tensors, which has found application in statistics, signal processing, psychometrics, linguistics and chemometrics. It was introduced by Hitchcock in 1927 and later rediscovered several times, notably in psychometrics. For this reason, the tensor rank decomposition is sometimes historically referred to as PARAFAC or CANDECOMP.
Consider a tensor space , where is either the real field or the complex field . Every (order-) tensor in this space may then be represented with a suitably large as a linear combination of rank-1 tensors: