四元数矩阵方程∑A~iXB_i=E

黄礼平

数学学报 ›› 1998, Vol. 41 ›› Issue (3)

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PDF(263 KB)
数学学报 ›› 1998, Vol. 41 ›› Issue (3) DOI: 10.12386/A1998sxxb0093
论文

四元数矩阵方程∑A~iXB_i=E

    黄礼平
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The Quaternion Matrix Equation A iXB i=E

    LiPing Huang
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摘要

本文指出并改正文[1]中的错误,给出弱特征多项式[2]与重特征多项式[3]间的显式关系,同时也给出行列式[2]与重行列式[4]间的显式关系,最后讨论了左特征值、右特征值、特征值和特征根之间的关系及最小多项式与弱特征多项式根之间的关系.

Abstract

Let H F be the generalized quaternion division algebra over a field F with  char F≠2. By using the adjoint matrix and the method of repersentation matrix, this paper obtains several necessary and sufficient conditions for existence of a solution or a unique solution to the matrix equation ki=0A iXB i=E over H F, and gives some explicit formulas of solutions.

关键词

矩阵方程 / 广义四元数矩阵 / 伴随矩阵

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黄礼平. 四元数矩阵方程∑A~iXB_i=E. 数学学报, 1998, 41(3) https://doi.org/10.12386/A1998sxxb0093
LiPing Huang. The Quaternion Matrix Equation A iXB i=E. Acta Mathematica Sinica, Chinese Series, 1998, 41(3) https://doi.org/10.12386/A1998sxxb0093
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