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 , 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.