TY  - JOUR
T1  - Rayleigh-Quotient Representation of the Real Parts, Imaginary Parts, and Moduli of the Eigenvalues of General Matrices
AU  - Kohaupt, Ludwig
PY  - 2020
DA  - August
Y2  - 2020
DO  - 10.33187/jmsm.669216
JF  - Journal of Mathematical Sciences and Modelling
PB  - Mahmut AKYİĞİT
WT  - DergiPark
SN  - 2636-8692
SP  - 55
EP  - 75
VL  - 3
IS  - 2
LA  - en
AB  - In the present paper, formulas for the Rayleigh-quotient representation of the real parts, imaginaryparts, and moduli of the eigenvalues of general matrices are obtained that resemble correspondingformulas for the eigenvalues of self-adjoint matrices. These formulas are of interest in Linear Algebraand in the theory of linear dynamical systems. The key point is that a weighted scalar product isused that is defined by means of a special positive definite matrix. As applications, one obtainsconvexity properties of newly-defined numerical ranges of a matrix. A numerical example underpinsthe theoretical findings.
KW  - Rayleigh quotient
KW  - Real and imaginary parts of eigenvalues
KW  - Moduli of eigenvalues
KW  - Asymptotic stability of dynamical systems
KW  - Circular damped eigenfrequencies
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UR  - https://doi.org/10.33187/jmsm.669216
L1  - https://dergipark.org.tr/en/download/article-file/1266281
ER  -