A topological approach to left eigenvalues of quaternionic matrices
Enrique Macías-Virgós, María José Pereira-Sáez · Linear and Multilinear Algebra · 2013
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 orders. In this paper, a different point of view is adopted by computing the topological degree of a characteristic map associated to the matrix and discussing the rank of the differential. The same techniques are extended to matrices, which are still lacking a complete classification.