2012/10/10 by E. Macías–Virgós, Macías-Virgós, E., M. J. Pereira‐Sáez +1
Computer Science · Mathematics · #15A18 #15A33 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1210.3009
openalex publication_date 2012/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that a 2× 2 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 3× 3 matrices, which are still lacking a complete classification.