Generalized Rayleigh-quotient Formulas for the Real Parts, Imaginary Parts, and Moduli of the Eigenvalues of Diagonalizable Matrices

Ludwig Kohaupt

doi:10.24297/jam.v14i2.7373

Generalized Rayleigh-quotient Formulas for the Real Parts, Imaginary Parts, and Moduli of the Eigenvalues of Diagonalizable Matrices

Authors

Ludwig Kohaupt Beuth University of Technology, Luxemburger, Berlin

DOI:

https://doi.org/10.24297/jam.v14i2.7373

Keywords:

Diagonalizable matrix, Real and imaginary parts of eigenvalues, Generalized Rayleighquotient formulas, Generalized numerical range, System matrix of a linear dynamical problem.

Abstract

In the present paper, generalized Rayleigh-quotient formulas for the real parts, imaginary parts, and moduli of the eigenvalues of diagonalizable matrices are derived. These formulas are new and correspond to similar formulas for the eigenvalues of self-adjoint matrices obtained recently. Numerical examples underpin the theoretical findings.

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Author Biography

Ludwig Kohaupt, Beuth University of Technology, Luxemburger, Berlin

Beuth University of Technology, Department of Mathematics, Luxemburger Str. 10, Berlin

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Published

2018-06-13

How to Cite

Kohaupt, L. (2018). Generalized Rayleigh-quotient Formulas for the Real Parts, Imaginary Parts, and Moduli of the Eigenvalues of Diagonalizable Matrices. JOURNAL OF ADVANCES IN MATHEMATICS, 14(2), 7702–7728. https://doi.org/10.24297/jam.v14i2.7373