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.

E. Macías-Virgós

M.J. Pereira-Sáez

Linear and Multilinear Algebra

线性和多线性代数发表了高质量的原创研究论文，推动了线性和多线性代数的研究，或者包括线性和多线性代数在数学和科学的其他分支中的新应用。线性和多线性代数还出版线性和多线性代数研究人员感兴趣的研究问题、调查文章和书评。适当的领域包括但不限于：域或环上的空间张量代数非负矩阵线性代数中的不等式组合矩阵理论数值线性代数表示理论李理论不变理论和算子理论线性和多线性代数的受众包括工业和学术数学家。

The journal "Linear and Multilinear Algebra" publishes high-quality original research papers aimed at advancing the study of linear and multilinear algebra, or exploring new applications of linear and multilinear algebra in mathematics and other scientific fields. Additionally, the journal features research questions, survey articles, and book reviews of interest to researchers in linear and multilinear algebra. Relevant areas include, but are not limited to: spaces over fields or rings, tensor algebra, non-negative matrices, inequalities in linear algebra, combinatorial matrix theory, numerical linear algebra, representation theory, Lie theory, invariant theory, and operator theory. The audience for this journal includes mathematicians from both industry and academia.

《Linear and Multilinear Algebra》期刊发表高质量的原创研究论文，旨在推动线性和多线性代数的研究，或探讨线性和多线性代数在数学及其他科学领域中的新应用。此外，期刊还刊登与线性和多线性代数相关的研究问题、调查文章和书评。适合的研究领域包括但不限于：域或环上的空间、张量代数、非负矩阵、线性代数中的不等式、组合矩阵理论、数值线性代数、表示理论、李理论、不变理论和算子理论。该期刊的受众包括工业界和学术界的数学家。

Category	Quartile
数学	4
数学, 数学	4

A topological approach to left eigenvalues of quaternionic matrices

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