Then, the optimal source training sequences are obtained from the first [N.sub.S] rows of the circular

orthogonal matrix while the optimal relay ones are obtained from the next [N.sub.R] rows, i.e.,

In addition, given an arbitrary

orthogonal matrix M [member of] [R.sup.rxr], it holds J(VM) = J(V), so J(V) is a cost function defined on Gr(r, n), and J(V) = J(V) = J [omicron] [pi](V).

Similarly, when wGK[L.sub.l] starts with [x.sub.1] and wGK[L.sub.u] starts with [y.sub.1]= [y.sub.1] = M[x.sub.1]/[[PARALLEL]M[x.sub.1][PARALLEL].sub.K], we have Y = Y and X = XQ with the

orthogonal matrix Q satisfying B = QB.

The next step of the algorithm was to actually make use of the

orthogonal matrixes created above and match the input PDF with the target PDF.

Taguchi [L.sub.27]

orthogonal matrix is formed as described in the Table 4.

Then we always have C = UH where H is positive semidefinite and positive definite if C has full rank, and U is [m.sub.1] x [m.sub.2] column

orthogonal matrix. In that last case, U is unique; see Higham [5].

The purpose of this study was to optimize the extraction conditions to simultaneously obtain the pectic polysaccharide from oriental tobacco leaves using

orthogonal matrix method.

It is shown how to build the

orthogonal matrix operator and how to use it in a process of curve reconstruction.

(1) Unit

Orthogonal Matrix is a unitized square matrix, the transpose of which equals to its inverse, which can be expressed as Q = [Q.sup.-1], QQ = QQ = E, where E is the identity matrix.

Let H be an M x N real matrix; then there exist an M x M

orthogonal matrix U, an N x N

orthogonal matrix V, and an M x N diagonal matrix S with diagonal entries [s.sub.1] [greater than or equal to] [s.sub.2] [greater than or equal to] ...

Theorem 2 (equivalence of an

orthogonal matrix to a rotation matrix [31]).

The first one is to find the best

orthogonal matrix H to remove the couplings among features and build new features.