Rayleigh quotient and left eigenvalues of quaternionic 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.

Keywords:

• Rayleigh quotient
• quaternion
• left eigenvalue

AMS SUBJECT CLASSIFICATIONS:

• 15A18
• 20G20

Acknowledgments

We are grateful to the two referees for useful remarks.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first two authors are partially supported by the Ministerio de Economía, Industria y Competitividad, Gobierno de España (MINECO) and FEDER research project [grant number MTM2016-78647-P]. The first author was partially supported by Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia [grant number ED431C 2019/10] with FEDER funds.