Abstract
R p ⊗ R = CΣ(A)⊗ C(C′) R ⊗ C(C′)⊥ CΣ(A)⊥ ⊗ C(C′), where Rp (Rn) represent the whole space, CΣ(•) denotes column vector space with inner product defined via Σ−1, C(•) if the standard inner product is used, ⊗ denotes the tensor product of linear spaces and represents the orthogonal sum of linear spaces. The decomposition is illustrated in Fig. 1. The estimation of the mean ABC is performed through projection of the data on the subspace CΣ(A) ⊗ C(C′). The subspace of Rp ⊗ C(C′)⊥ and CΣ(A)⊥ ⊗ C(C′) are the spaces where residuals are constructed via projections, i.e.
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