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关于矩阵表示秩的研究及应用

RESEARCH ON THE RANK OF MATRIX EXPRESSIONS WITH APPLICATIONS
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摘要 考虑四元数体上的两个矩阵表达式A—BXB*-CY—Y*C*和A—BXB*-CY+Y*C*,其中A是四元数上的埃尔米特矩阵或是斜埃尔米特矩阵.在四元数体上研究了这两个线性矩阵表达式的最大秩和最小秩,并且给出了满足最小秩时X和Y的一般形式.作为应用,通过矩阵秩的方法得到了一四元数矩阵方程相容的充要条件. Considering A - BXB * - CY - Y * C * and A - BXB * - CY + Y* C * as two linear matrix expressions over quaternion algebra, where A is an Hermitian or skew - Hermitian matrix, we establish the formula of the maximal and minimal ranks of quaternion matrix expressions mentioned above. Moreover, we consider how to choose X and Y such that the two expressions attain the minimal possible ranks. As an application, we get the necessary and sufficient conditions for the consistence of quaternion matrix equation.
出处 《山东师范大学学报(自然科学版)》 CAS 2013年第3期9-11,15,共4页 Journal of Shandong Normal University(Natural Science)
基金 山东省高等学校科技计划项目(J09LA55) 齐鲁师范学院青年基金资助项目(2012L1001).
关键词 矩阵表达式 埃尔米特矩阵 最小秩 最大秩 matrix expressions Hermitian matrix minimal rank maximal rank
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参考文献7

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