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math.RA2010
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…
math.RA2009
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…
math.RA2008
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…