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arXiv · 2603.00018

Computing Left Eigenvalues of Quaternion Matrices

Michael Sebek
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Abstract

We present a practical Newton-based method for computing left eigenvalues of quaternion matrices. It uses only standard real/complex linear-algebra kernels via embeddings and applies to matrices of any size. Extensive tests on literature examples and benchmark ensembles, together with a compact MATLAB reference implementation, demonstrate reproducible, certificate-based computations up to size 64x64, including the detection of multiple spherical components and non-generic phenomena such as more than n isolated left eigenvalues and left-spectrum deficiency.

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Michael Sebek. 2026-02-02. Computing Left Eigenvalues of Quaternion Matrices. https://arxiv.org/abs/2603.00018

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