An equivalent definition for multiplicities of a quaternionic eigenvalue

2022/12/20 by Stefano Spessato, Spessato, Stefano
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2212.10195

openalex publication_date 2022/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce two definitions for algebraic and geometric multiplicities of a quaternion right eigenvalue. This definitions are equivalent to the classical ones. However, differently from the usual definitions, the notions of root subspace and Jordan form of a quaternion matrix are not required and all the properties can be proved easily.

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