diagonalize

One step of the block Jacobi method is needed to diagonalize A.

Here a finite Hamiltonian matrix is obtained and one can diagonalize it, find the smallest eigenvalue [E.sub.0] and its associated eigenfunction [T.sub.0].

The physical interpretation of Proposition 3 is that in order to diagonalize the correlation matrix of the MIMO channel and at the same time to obtain the largest possible link power then the columns of the matrix T' [cross product] R should be chosen so that they equal the eigenvectors of the matrix [R.sub.m] corresponding its [M.sub.s] strongest and distinct eigenvalues.

Step 1 Diagonalize [S.sup.F] = [TT.sup.*] = U [[LAMBDA]U.sup.*], where [LAMBDA] = diag([[lambda].sub.i])i.

Humans love to take shortcuts; they love to diagonalize.

Viable candidates include the Bohm theory which, selecting position as the preferred determinate observable, solves the measurement problem if measurement outcomes are without exception recorded in positions, and Modal Interpretations which, making the preferred determinate observable state-dependent, solve the measurement problem if measurement outcomes are without exception recorded in observables whose eigenbases diagonalize the post-measurement reduced states of participant apparatus.

The eigenmodes diagonalize the integral equation kernels and are independent of incident field [6].

Using 5 x 5 unitary matrices [64, 65], one can diagonalize the neutrino mass matrix [M.sub.[nu]] in (5).

As mentioned, we diagonalize the permeability tensor to obtain the principal permeability components and the principal directions [theta] and [mathematical expression not reproducible].

Let X = [[X.sub.1] [X.sub.2]] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be non-singular matrices which simultaneously diagonalize the Hermitian matrix pairs (H, M) and ([??], M) as in (2.2) and (2.4), where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are indefinite and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is positive definite.

As the permeability tensor in Equation (7) is symmetrical, we can always diagonalize it [13].

For the evolution of the energy level, it is necessary to diagonalize the Hamiltonian [[??].sub.l], which can be accomplished by introducing the vector Bose-operators [[??].sup.+.sub.[??]] and [[??].sub.[??]] [12]:

In fact, we only need the following bivariate special case of it (when we diagonalize all [x.sub.i] = x and [y.sub.i] = y):