| 一类四元数受限矩阵表达式的最大秩（英文） |
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| 引用本文： | 连德忠. 一类四元数受限矩阵表达式的最大秩（英文）[J]. 数学研究, 2012, 45(2): 144-158 |
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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： | supported by the Technological Foundation of Fujian Educational Committee(JB08236) |
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| 摘 要： | 确立了一类分块矩阵M11 M12 XM21 M22 M23Y M32 M33的最大秩公式,其中,X和Y是两个受限于四元数线性矩阵方程A_1X=C_1,XB_1=C_2,A_3XB_3=C_3,A_2Y=D_1,YB_2=D_2.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另一四元数二次矩阵方程组解集的条件。
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| 关 键 词： | 四元数代数 分块矩阵 最大秩 二次矩阵表达式 解集 |
Maximal Rank of A Kind of Quaternion Matrix Expressions Subject to Some Consistent Systems |
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| Lian Dezhong. Maximal Rank of A Kind of Quaternion Matrix Expressions Subject to Some Consistent Systems[J]. Journal of Mathematical Study, 2012, 45(2): 144-158 |
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| Authors: | Lian Dezhong |
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| Affiliation: | Lian Dezhong (Department of Mathematics and Computer Science, Longyan Institute,Longyan Fujian,364000) |
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| Abstract: | We establish the formulas of the maximal rank of a 3x3 partial banded block matrix where X and Y are a pair variant quaternion matrices subject to linear quaternion matrix equations A1X = C1,XB1=C2,A3X B3=C3,A2Y = D1,Y B2=D2. As an application,we compare the solution set of the linear matrix equations mentioned above and the solution set of the quadratic system A1X = C1,X B1 = C2,A3XB3=C3,A2Y = D1,Y B2 = D2,X PY = J over the quaternion algebra. |
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| Keywords: | Quaternion algebra Partial banded block matrix Maximal rank Quadratic matrixexpression Solution set |
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