# 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.
References in periodicals archive ?
This shows that diagonalization bears the potential of substantially reducing the computational cost in a Krawczyk-type enclosure method.
For large n the process of diagonalization requires a lot of storage and time of calculation.
Following Kac, the analysis of the Ehrenfest urn is traditionally developed from an explicit diagonalization of the (N + 1) x (N + 1) "Kac matrix",
The system (25) is decoupled by applying the diagonalization method of [13] to matrix M, which transforms it into a diagonal mass matrix, [M.
The use of several thousand terms in a wave function leads to memory problems arising from storage of the matrix elements prior to the matrix diagonalization step at least for dense matrices that result from the introduction of interelectronic coordinates into the wave function.
9 Filter Diagonalization Methods for Time-Domain Signals (A.
T]A) is diagonalized by the discrete cosine transform matrix and this diagonalization is reused through the iterations.
They continue to present material in a two-semester format, the first on computability theory (enumerability, diagonalization, Turing compatibility, uncomputability, abacus computability, recursive functions, recursive sets and relations, equivalent definitions of computability) and basic metalogic (syntax, semantics, the undecidability of first-order logic, models and their existence, proofs and completeness, arithmetization, representability of recursive functions, indefinability, undecidability, incompleteness and the unprobability of inconsistency).
33) is decoupled by applying the diagonalization method of [9] to matrix M which transforms it into a diagonal matrix [M.
In practice, the Zeeman shifts are normally much larger than the Stark shifts, so that HE does not affect the diagonalization.
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