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2015•Zeitschrift für Naturforschung AOpen access

Eigenvalue Problem, Spin Systems, Lie Groups, and Parameter Dependence

Willi-Hans Steeb, Yorick Hardy

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Abstract

Abstract We study square matrices F(α) over ℂ with α∈ℝ, where the eigenvalues depend on the parameter α but not the eigenvectors, and vice versa, where the eigenvectors depend on the parameter α but not the eigenvalues. We derive sufficient conditions for such properties. Applications to Lie groups and spin systems are provided. Both normal and nonnormal matrices are investigated.

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Abstract We study square matrices F(α) over ℂ with α∈ℝ, where the eigenvalues depend on the parameter α but not the eigenvectors, and vice versa, where the eigenvectors depend on the parameter α but not the eigenvalues. We derive sufficient conditions for such properties. Applications to Lie groups and spin systems are provided. Both normal and nonnormal matrices are investigated.

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Available abstract

Abstract We study square matrices F(α) over ℂ with α∈ℝ, where the eigenvalues depend on the parameter α but not the eigenvectors, and vice versa, where the eigenvectors depend on the parameter α but not the eigenvalues. We derive sufficient conditions for such properties. Applications to Lie groups and spin systems are provided. Both normal and nonnormal matrices are investigated.

Key concepts: Eigenvalues and eigenvectors, Mathematics, Spin (aerodynamics), Eigenvalue perturbation, Pure mathematics, Eigenvalues and eigenvectors of the second derivative, Applied mathematics, Mathematical analysis

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