| 一类四元数矩阵三次方程的可解性(英文) |
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| 引用本文： | 连德忠. 一类四元数矩阵三次方程的可解性(英文)[J]. 数学研究, 2012, 0(4): 390-403 |
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| 作者姓名： | 连德忠 |
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| 作者单位： | 福建龙岩学院数计院系,福建龙岩364000 |
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| 基金项目： | Foundation item： This research was supported by the Technological Foundation of Fu.jian Educational Committee （JB08236）. |
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| 摘 要： | 确立了某类分块矩阵[M（11） M12 XM21 Y M23Z M32 M33]的最大秩公式,其中,X,Y和Z是三个受限于四元数线性矩阵方程A1X=C1,XB1=C2,A2Y=D1,YB2=D2,A3Z=E1,ZB3=E2的变量矩阵.作为该公式的一项应用,我们推导出上述矩阵方程解集等同于某类四元数三次矩阵方程组A1X=C1,XB1=C2,A2Y=D1,YB2=D2,A3Z=E1,ZB3=E2,XYZ=J解集的条件.
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| 关 键 词： | 四元数域 分块矩阵 线性矩阵方程 最大秩 三次矩阵方程 解集 |
The Solvability of a Kind bf Cubic Quaternion Matrix Equations |
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| Lian Dezhong. The Solvability of a Kind bf Cubic Quaternion Matrix Equations[J]. Journal of Mathematical Study, 2012, 0(4): 390-403 |
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| Authors: | Lian Dezhong |
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| Affiliation: | Lian Dezhong (College of Mathematics and Computer Science, Longyan University, Longyan Fujian, 364000) |
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| Abstract: | In this paper, we establish the formulas of the maximal-rank of a 3×3 partial banded block matrix [M11 M12 X M21 Y M23 Z M32 M33] where X, Y and Z are three variant quaternion matrices subject to linear matrix equations A1X = C1, XB1 = C2, A2Y = D1, YB2 = D2, A3Z = El, ZB3 = E2 As an application, we compare the solution set of the cubic system A1X = C1, XB1 = C2, A2Y = D1, YB2 = D2, A3Z = El, ZB3 = E2, XYZ = J with the solution set of its linear partial equations over the quaternion field |
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| Keywords: | Quaternion field Partial banded block matrix Linear matrix equations Maximalrank Cubic matrix equation . Solution set |
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