The second involves taking advantage of the structure of the resulting matrices when transformations are accumulated onto the

identity matrix. The speedup is particularly noticeable for smaller bandwidths where the loop interchange idea has no impact.

Therefore, E is the

identity matrix if [Lambda] = I, so any epistasis is sufficient to allow for canalization somewhere along a contour.

Furthermore, if we let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], denote the

identity matrix of size [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then it may be observed that this algorithm operates by implicitly incorporating permutations so that each term in the product becomes

where [N.sub.R] is the number of receiving antennas, H is the channel matrix, the trace operator denotes the sum of the main diagonal elements of a matrix, [mathematical expression not reproducible] is the

identity matrix with dimension [N.sub.R] x [N.sub.R], E is the expected value, and det is the determinant, respectively.

The inverse-FORM algorithm and the intermediate algorithm mentioned in previous section become identical if the Hessian of the Lagrangian is approximated as the

identity matrix in every iteration.

where I denotes an

identity matrix and [alpha] > 0 is a parameter.

Defining [[zeta].sub.r] as the rth row of the [n.sub.y]-dimensional

identity matrix, we have

in which [I.sub.t] is a t x t

identity matrix, then [P.sub.t], [Q.sub.t], [S.sub.t], [R.sub.t] are unitary matrices.

The presuppositions assumed in relation to the vectors y, a, m and e were: E[y] = X[beta]; Var(a)=[A.sub.[direct sum]] [G.sub.a], Var(m)=A [direct sum] [G.sub.m], Var(e)=I [direct sum] [R.sub.e], where [G.sub.a] is the matrix of the direct additive genetic covariance; [G.sub.m] is the matrix of the maternal additive genetic covariance; [R.sub.e] is the matrix of the residual covariance; A is the numerator matrix of genetic additive relations; I is the

identity matrix; and [direct sum] is the direct product between matrixes.

The matrix D(z) is said to be column monic if its highest column degree coefficient matrix is the

identity matrix.

The group multiplication of GL(n, R) is the usual matrix multiplication, the inverse map takes a matrix A on GL(n, R) to its inverse [A.sup.-1], and the identity element is the

identity matrix I.

We use I for the

identity matrix and J:= [([[delta].sub.i,n+1-i]).sub.i,j=1, ..., n] for the exchange, or "flip" matrix.