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math.RA2020
Rayleigh quotient and left eigenvalues of quaternionic matrices
E. Macías-Virgós, M. J. Pereira-Sáez, Ana D. Tarrío-Tobar
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 ri…
math.RA2012
A topological approach to left eigenvalues of quaternionic matrices
E. Macías-Virgós, M. J. Pereira-Sáez
It is known that a quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher…