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arXiv · 2203.15919

On the existence of left and right eigenvalues

Bamdad R. Yahaghi
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Abstract

In this note, we consider arbitrary finite-dimensional real algebras containing a copy of complex numbers. It is proved that matrices with entries from an arbitrary finite-dimensional real algebra containing a square root of negative one in its left (resp. right) associate set have left (resp. right) eigenvalues. A quick consequence of our main result is the existence of left and right eigenvalues for matrices with entries from finite-dimensional alternatives algebras containing a copy of complex numbers, e.g., octonions, and more generally matrices with entries from the real Cayley-Dickson algebras.

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Bamdad R. Yahaghi. 2022-03-29. On the existence of left and right eigenvalues. https://arxiv.org/abs/2203.15919

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