# 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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Algorithm 1 again fails because it attempts to diagonalize A, obtaining a matrix V with condition number K(V) = 2.
In other words, the transform that diagonalizes the matrix A is known only in special cases, such as in the case of strongly symmetric PSFs and reflective and anti-reflective BCs (see [9, 12] and references therein).
Therefore to complete our task we need to diagonalize the operator H, i.
We diagonalize this self-adjoint bounded operator and find its spectrum with the aid of the second operator I, which corresponds to a q-difference equation for the same set of polynomials.
Compute the matrix V of eigenvectors which diagonalizes the covariance matrix C:
it diagonalizes [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
In a basis which diagonalizes [[left and right arrow][epsilon]] ([[vector].
An angular basis set is used which diagonalizes the rotational (J > 0) part of the total kinetic energy.
j] a matrix that diagonalizes simultaneously the matrices [?
A primitive angular basis set is constructed which diagonalizes the rotational (J > 0) kinetic energy operator; subsequently, this basis is contracted through a series of diagonalizations of smaller Hamiltonian matrices.
And (to a fair approximation) a preferred basis will arise naturally, within the quasi-classical domain, as the basis which, under coarse-graining, diagonalizes the decohering variables.

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