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Spectrum of a matrix

About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.


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Journal ArticleDOI
TL;DR: In this paper, the SU(3) model of Elliott for an arbitrary oscillator n -shell is considered and an explicit expression for the eigenvalues of the generalized density matrix (GDM) in the case of low-lying multiplets is found.

1 citations

Journal ArticleDOI
TL;DR: In this paper, it is shown that numerical deflation, in the form of adding singularities near the extracted eigenvalues, allows determination of a prescribed number of different eigen values from a fixed-point initial guess.

1 citations

Journal Article
TL;DR: In this article, the estimation for eigenvalues of matrices and its application in stability theory is discussed and a sufficient condition that a linear time-invariant system is asymptotically stable in equilibrium position is presented.
Abstract: The purpose of this paper is to discuss the estimation for eigenvalues of matrices and its application in stability theoryWe prove that all the eigenvalues of any complex matrix are located in one diskAfter that,we present a sufficient condition that a linear time-invariant system is asymptotically stable in equilibrium positionSome numerical examples are given

1 citations

01 Jan 1993
TL;DR: In this article, a minimum principle is established for the radial Dirac Hamiltonian for any potential, which uses an r-dependent unitary transformation to decouple the equations for the large and small components of the radial wavefunction; the transformed equation maps to an ordinary Sturm-Liouville equation whose mini- _- mum principle ensures convergence of the eigenvalues from above.
Abstract: A minimum principle is established for the radial Dirac Hamiltonian for any potential. This principle uses an r-dependent unitary transformation to decouple the equations for the large and small components of the radial wavefunction; the transformed equation maps to an ordinary Sturm-Liouville equation whose mini- _- mum principle ensures convergence of the eigenvalues from above. As a concrete and typical example of the application of the principle, basis sets are developed for the Coulomb potential; these sets may be built out of any complete sequence of functions. The positive matrix eigenvalues converge from above to the exact bound-state eigenvalues, the negative eigenvalues converge from below to -mc2, and the wavefunctions corresponding to positive eigenvalues converge in mean- square to the exact bound-state wavefunctions. For the Coulomb potential only, bases of relativistic Sturmian functions are found in which the matrix eigenvalue problem is banded instead of full, and can be solved quickly and stably on a com- - puter even for as many as 4800 basis vectors. An analytic formula is given which expresses the eigenvalues and eigenvectors in terms of the Pollaczek polynomials _ -- an&&eir-zeros. A simple recursion is presented that will evaluate in any Sturmian .

1 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
20229
20202
20193
20187
201731