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.