where the

submatrix [H.sub.i] is a (q -1) x n(q -1) matrix containing n CPMs and each [A.sub.ij].

More generally, the number of principal minors that must be checked is reduced when a definite principal

submatrix can be identified.

While in the skeleton approximation (SA) theory [10], there is a nonsingular r x r

submatrix [??] in [Z.sub.far].

Expressing it a bit more formally in terms of triads (the upper triangle of a PC

submatrix 3 x 3), we have

Then, [P.sub.i] alternatively employs the update rules (5) and (6) to obtain its private coefficient

submatrix [[??].sub.i] (Statement (7)) and basis

submatrix [[??].sub.i] (Statement (10)) until the termination condition for the iteration is satisfied.

of A is said to be a column basis

submatrix of A (a row basis

submatrix of A, a basis

submatrix of A, resp.).

In other words, the necessary and sufficient condition for the solution of (3) is that, for any

submatrix of the binary random matrix, if the number of rows of it is greater than the number of columns, the

submatrix is full column rank.

A distribution of every mxm

submatrix in the interaction matrix is calculated by using the intervals [2.0-2.2), [2.2-2.4), [2.4-2.6), [2.6-2.8), and [2.8-3.0].

with each

submatrix corresponding to a single time-step.

Now, by theorem 7.1, there exists a 16m x 16m

submatrix B of M(P) with an odd det B, from lemma 2.3 the system PX = K has a solution over Z[[Q.sub.16]].

For a matrix A, let [a.sub.ij], [A.sub.k], [??], and A* denote the i, j entry, the upper-left k x k

submatrix, the upper-left (k + 1) x k

submatrix, and the conjugate transpose of A, respectively.

"Each plugin provides a single or dual 128 x 4

submatrix with the capability to connect its Y axis to one of 12 or six analog buses (depending upon the plugin model type)/' he said, thereby providing a high degree of flexibility in matrix configuration and making parallel testing much simpler.