At step k the block Jacobi method

diagonalizes the pivot submatrix of [A.sup.(k)].

Now, since we are seeking to

diagonalize [R.sub.h], then (34) must be satisfied.

As we mentioned before, computations in Step 1 require us to

diagonalize the matrix [TT.sup.*].

Another unitary matrix T = diag([U.sub.[nu]], [U.sub.R]) matrix again

diagonalizes the mass matrices in the light and heavy sectors are appearing in the upper and lower block of the block diagonal matrix, respectively.

However, when the cyclic frequencies are a priori known, the operation is much more easier; it is reduced to computing [R.sup.[xi].sub.x]([tau]) at different time lags for each cyclic frequency {[[xi].sub.i]/ i = 1, ..., n} then to

diagonalize simultaneously the set built

Let H = GJG*, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and M be positive definite, and let X = [X.sub.1] [X.sub.2] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be non-singular matrices from (2.2) and (2.4) which simultaneously

diagonalize the pairs (H, M) and ([??], M), respectively.

We

diagonalize the matrix U by choosing such functions |[[bar.[psi].sub.i> for which the matrix <[[bar.psi].sub.j]|v|[[bar.[psi].sub.k> (and hence the corresponding matrix U) is equal to none.

zigzag scanning (prior to run-length)

diagonalize data from (0, 0)

where T can

diagonalize both [[??].sub.x] and [[??].sub.y] in a similarity transformation.

In IEEE 802.11ac, the channel matrix is compressed with a sequence of angles of Givens rotation matrices, which

diagonalize a given channel matrix.

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.[??]] [11]:

For any system except for the very smallest (less than about 1000 atoms), iterative techniques, such as the Arnoldi method (10), must be used to

diagonalize the system Hamiltonian and only those eigenstates near the fundamental gap are found.