diagonalize


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diagonalize

[dī′ag·ən·ə‚līz]
(mathematics)
To convert a square matrix to a diagonal matrix, usually by multiplying it on the left by a second matrix A of the same order, and on the right by the inverse of A.
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References in periodicals archive ?
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.