Rayleigh quotient and left eigenvalues of quaternionic matrices
E. Mac\'ias-Virg\'os, M.J. Pereira-S\'aez, Ana D. Tarr\'io-Tobar
TL;DR
This paper investigates the properties of the Rayleigh quotient for quaternionic Hermitian matrices and explores relationships between left and right eigenvalues of such matrices and symplectic matrices.
Contribution
It introduces new properties of the Rayleigh quotient in the quaternionic setting and establishes links between left and right eigenvalues of Hermitian and symplectic matrices.
Findings
Properties of the Rayleigh quotient for quaternionic Hermitian matrices
Relationships between left and right eigenvalues of Hermitian matrices
Connections between eigenvalues of symplectic matrices
Abstract
We study the Rayleigh quotient of a Hermitian matrix with quaternionic coefficients and prove its main properties. As an application, we give some relationships between left and right eigenvalues of Hermitian and symplectic matrices.
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Taxonomy
TopicsMatrix Theory and Algorithms · Advanced Topics in Algebra · Algebraic and Geometric Analysis