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<p>We establish an analogue of the Fundamental Theorem of Algebra for polynomial matrix equations, where both the coefficient matrices and unknown matrix are <i>Q</i>-circulant matrices that were introduced in [H. Li, W. Zhang, P. Yuan, <i>Comput. Appl. Math.</i>, 43 (2024), Paper No. 154]. The results of this paper generalize the results in [V. M. Abramov, <i>Amer. Math. Monthly</i>, 132 (2025), 356–360] established for circulant matrices.</p>

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Extension of the fundamental theorem of algebra for polynomial matrix equations over Q-circulant matrices

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Hongjian Li

摘要

We establish an analogue of the Fundamental Theorem of Algebra for polynomial matrix equations, where both the coefficient matrices and unknown matrix are Q-circulant matrices that were introduced in [H. Li, W. Zhang, P. Yuan, Comput. Appl. Math., 43 (2024), Paper No. 154]. The results of this paper generalize the results in [V. M. Abramov, Amer. Math. Monthly, 132 (2025), 356–360] established for circulant matrices.