2 citations · 2 across the 6 of their papers we have counts for
7 papers
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…
Non-linear Morse-Bott functions on quaternionic Stiefel manifolds
Enrique Macías-Virgós, María José Pereira-Sáez, Daniel Tanré
In the Stiefel manifold , we replace Frankel linear height function by a quadratic one. We prove this is still a Morse-Bott function, whose structure of critical levels pr…
Cayley Transform on Stiefel manifolds
Enrique Macías-Virgós, María José Pereira-Sáez, Daniel Tanré
We define a Cayley transform on Stiefel manifolds. Applications to the Lusternik-Schnirelmann category and optimisation problems are presented.
Classification of the relative positions between a hyperboloid and a sphere
M. Brozos-Vázquez, M. J. Pereira-Sáez, M. J. Souto-Salorio +1
We characterize all possible relative positions between a hyperboloid of one sheet and a sphere through the roots of a characteristic polynomial associated to these quadrics. The c…
Characteristic functions and Hamilton-Cayley theorem for left eigenvalues of quaternionic matrices
E. Macías-Virgós, M. J. Pereira-Sáez
We introduce the notion of characteristic function of a quaternionic matrix, whose roots are the left eigenvalues. We prove that for all matrices and for ma…
Symplectic matrices with predetermined left eigenvalues
E. Macías-Virgós, M. J. Pereira-Sáez
We prove that given four arbitrary quaternion numbers of norm 1 there always exists a symplectic matrix for which those numbers are left eigenvalues. The proof is const…
Left eigenvalues of symplectic matrices
E. Macías-Virgós, M. J. Pereira-Sáez
We obtain a complete characterization of the symplectic matrices having an infinite number of left eigenvalues. Previously, we give a new proof of a result from Huang a…