Subsequently, the matrix S = S W - 1 S B is subjected to the eigen decomposition S = ΦΛΦ T, where Λ = diag λ1,..., λ M ) is the matrix with the ordered eigenvalues along the diagonal and Φ = [u1|... |u M ] is the matrix with the correspondingly ordered eigenvectors as columns.
They are either irreducible or zero matrix with order 1, ∑ t = 1 K n t = n.
(S^{-1}) is the inverse matrix of covariance between two variables and it is square matrix with order two.
(S^{-1}) is the inverse matrix of covariance between two variables times ((lambda /2-lambda)) and it is square matrix with order two.
When A is an irreducible matrix and a zero matrix with order 1, for unity, denote A = [ A 11 ], where n 1 = n and N 1 = N. Denote α = ⋃ n t ≥ 2, 1 ≤ t ≤ K N t, θ A = { a i i A ∣ i ∈ N ∖ α }.
Besides, we assume that Y = Y 1, Y 2, …, Y m, and Y i = A X i + μ, then Y = m A ( 1 m X ) + μ ( II m ′ ⊗ I p ), Γ n × n ( 1 m X ) = d 1 m X, E ( 1 m X ) ( 1 m X ) ′ = I, where Γ is a random orthogonal matrix with order n.
Besides, d denotes identical distribution, S denotes X X ′, and all Γ n × n ∈ o ( n ) are orthogonal matrices with order n.
Based on the business process stream H, its autocorrelation matrix with N * N order is constructed as shown in Fig. 8.
The GP(I -zones are coherent wI -zonesareminum matrix, with internal ordering of Zn and Al/Mg on the matrix latticoherentested to be based on AuCu(I)-type sub-unit, and anti-phase boundaries.
A is a numerator relationship matrix across all animals inferred from the pedigree (n = 3 360), and I is an identity matrix with an order equal to the number of observations in y.
