Where [P.sub.NS.sup.(i)] is the projection matrix of the

nullspaces of class i and P is the projection matrix of the subspace of the total scatter matrix.

[A.sub.n]) [(A).sup.T] Trace of A [(A).sup.H] The right-hand

nullspace of A [(A).sup.-1] A block-diagonal matrix with the i-th diagonal block specified by [A.sub.i] where n is an integer Table 2.

Then we can obtain [[bar.v].sub.l], from the

nullspace of [Q.sup.T][[bar.H].sub.l] [member of] [R.sup.3 x 4].

To this end, P must be chosen as an oblique projection with the property that when its

nullspace Z is A-invariant, so is its range [[??].sup.[perpendicular to]].

h) If the

nullspace of [B.sup.T] is an invariant subspace of A, then M = 0, i.

WHITE, Substructuring methods for computing the

nullspace of equilibrium matrices, SIAM J.

Moreover, deriving a conforming approximation of the

nullspace (2.7) is difficult, which leaves the saddle-point problem (2.5) as the preferred setting for the constrained minimization.

As it will be seen in Section 2, the use of algebraic methods will allow us to formulate the problem of inversion in terms of the computation of the

nullspace of a Sylvester matrix of order l and rank l - 1, a task which for accuracy reasons is carried out by using the singular value decomposition.

However, block l-l =1-1 contains the grad-div operator [nabla][nabla]*, whose

nullspace consists of divergence-free functions.

handles the

nullspace structure of the discretization matrices.

Finally, [rho](A) is the spectral radius of [A,.sup.t] denotes the transpose, Ker is the

nullspace, and Im is the range.

This eigenvalue problem has N finite solutions [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and m - N indeterminate eigenvalues corresponding to eigenvectors [{[e.sub.i].sup.m.sub.i=N+1] spanning the

nullspaces of [bar.C] and [bar.CA].