# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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The limitations of SUTCCSP have been addressed in this study due to the loss of the correlation information during the simultaneous diagonalization process of the covariance and pseudocovariance matrices.
In this paper, we applied a diagonalization method with nested method of successive averages (MSA) to solve the aforementioned VI problems.
Note that both of the intersection matrices of E and F are negative definite again by diagonalization of the intersection matrices.
Although the calculation was performed using the FEM in all cases, the spectral scheme that involves the diagonalization of the Hamiltonian matrix resulting from expansion (6) was also applied and the corresponding results appear superimposed to the FEM ones in Figure 2(a), showing a remarkably good coincidence.
have solved the problem of blind identification of FIR MIMO systems driven by cyclostationary inputs whose cyclic frequencies are pairwise distinct using joint block diagonalization based on BFGS method in .
VASP code performs an iterative diagonalization of the Kohn-Sham Hamiltonian via unconstrained band-by-band minimization of the norm of the residual vector to each eigenstate and via optimized charge density mixing routines.
Naturally, as the dimensionality of the matrices becomes very high, i.e., several tens or hundreds of thousands and above, explicit methods of function evaluation, like exact diagonalization, break down and approximations must be made.
Given N nodes of the ENM, NMA requires a diagonalization of a 3N x 3N matrix of second derivatives of the potential energy (Hessian matrix), which is performed via eigenanalysis of the Hessian matrix.
Proof: Either analogous to the proofs of Corollary 2.2 and Theorem 3.3 or by a standard diagonalization argument.
The simplest variant is associated with the explicit construction of the solution using the known eigenvalues and eigenfunctions of the elliptic operator with diagonalization of the corresponding matrix [5,14,15].

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