The optimal solutions need to give equality in (48) and thus Lemma 3 gives that V Σ Σ H V H is diagonal and equal to Σ Σ H. Lemma 1 then implies that V = diag v1,1, …, vn,n) with |vi,i| = 1 for i = 1, …, n.
In our formulation, K is set to be equal to M for practical reasons, and P d 's are diagonal matrices.
The approach is fully efficient, because the variance-covariance matrix of the vector of means y is diagonal with elements equal to var e) [ 14].
When individuals are unrelated, the gametic deviations of those individuals are also uncorrelated, thus cosegregation information can also be combined with the residual, (17) This, however, results in the residual variances to be heterogeneous, (18) Residual covariance matrix R * is diagonal with element equal to when individuals are unrelated.
With uncorrelated taps, the autocorrelation matrix is block diagonal and there are blocks along the diagonal, each is equal to as defined in (5).
For both the 4 and X the rates of genetic nondisjunction and cytological malorientation were almost completely correlated (r = 0.970 for X and r = 0.972 for 4, Pearson correlation coefficient) and not far from the prediction that the two measurements should be equal (diagonal lines).
Upper diagonal figures are D' and lower diagonal figures are r.
x i ∼ N (m, Σ ) (9) y j ∼ N (m, Σ ), where, m = (0, …, 0 ) ′ and Σ is a diagonal matrix with diagonal elements all equal to 10,000.
with a i = ∏ j = 1 M σ i, j M, where the sequence { σ i, j } j = 1 M is the singular value of H i. U1 and U2 are unitary matrices of dimensions N1 × N1 and N2 × N2, respectively, D1 and D2 are generalized upper triangular matrices with equal diagonal elements, and † denotes the conjugate transpose.
By Eq. (19), ∇2 F ε (v) for v lying in the first octant of (mathbb {R}^{n}) is a diagonal matrix and is equal to (-frac {1}{epsilon ^{diag}xt {diag}(e^{-frac {v_{1}}{epsilon }}, e^{-frac {v_{2}}{epsilon }}, ldots, e^{-frac {v_{n}}{epsilon }})) or −diag((v 1+ε)−2, v 2+ε)−2,…(v n +ε)−2) which corresponds to F ε being the Mangasarian or the Log-Det function.
