In Figures 9(a)-9(f), we show the fill for i =1 and i =2 for an example with n = 13 and k = 3 assuming Q is initially the

identity matrix. Above some of the affected columns in each figure we indicate which transformation in Figures 1(a)-c is being used.

In other words, when E is not a multiple of the

identity matrix (a matrix with ones along the diagonal and zeros everywhere else).

where [n.sub.1] is the order of A; [n.sub.2] the order of B; [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the

identity matrix of order [n.sub.i] and "+" represents the usual operation of matrix addition.

where: [[Epsilon]] is the n x n matrix of all own and cross price elasticities of demand in the economy; [I] is the n x n

identity matrix; and [[Phi]] and [([Omega] - [Phi])] are n x 1 matrices of [[Phi].sub.u]'s and ([Omega].sub.u] - [[Phi].sub.u])'s, u = 1, ..., n.

for 0[less than or equal to]s[less than or equal to]t<[infinity], I being the

identity matrix.

This will yield the

identity matrix. Z+.x *Z 1 0 0 1

Common computation method shared in the application of these two techniques is that one have a destination estimate [??] and an initial matrix [??], which are usually scaled

identity matrix and empirical covariance, respectively.

With I we denote the

identity matrix. Given a vector v [member of] [C.sup.N], we use diag(v) for the matrix with v in its diagonal entries and zero elsewhere.

where [I.sub.n_1] is the

identity matrix of order n - 1.

(ii) Using an

identity matrix as channel matrix--with no fading applied ("baseline" measurement): this measurement can be seen as if the UE would directly be connected to the BSE by wires.

Hence, further modifications were made to arrive at the hybrid algorithm that uses the

identity matrix in few iterations and the BFGS update formula in other iterations for approximating the Hessian of the Lagrangian.

where [G.sub.d] is the (co)variance matrix of random direct additive genetic effects; [G.sub.m] is the (co) variance matrix of random maternal additive genetic effects; Q is the (co)variance matrix of random permanent maternal environment effects; R is the (co)variance matrix of random residual effects, A is the numerator relationship matrix, [I.sub.v] is the

identity matrix with order v, where v is the number of mothers, [I.sub.n] is the

identity matrix with order n, where n is the number of observations, and [R] is the Kronecker product operator.