| 四元数体上矩阵方程AXA*=B的非负定解 |
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| 引用本文： | 李桃生,赵小妹,孙志敏. 四元数体上矩阵方程AXA*=B的非负定解[J]. 华中师范大学学报(自然科学版), 2002, 36(4): 403-408 |
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| 作者姓名： | 李桃生 赵小妹 孙志敏 |
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| 作者单位： | 华中师范大学,数学系,武汉,430079 |
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| 摘 要： | 讨论了四元数体上矩阵方程AXA^*=B的非负定解，解决了以下问题：（1）给出了四元数体上矩阵方程AXA^*＝B存在非负定解的充分必要条件；（2）当矩阵方程AXA^*=B的非负定解，给出了求X的秩的公式以及X为最小秩或最大秩解的条件。
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| 关 键 词： | 矩阵方程 非负定解 四元数体 非负定矩阵 正定矩阵 满秩分解 1－逆 |
Nonnegative definite solution of the matrix equation AXA*=B over quaternion field |
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| Abstract. Nonnegative definite solution of the matrix equation AXA*=B over quaternion field[J]. Journal of Central China Normal University(Natural Sciences), 2002, 36(4): 403-408 |
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| Authors: | Abstract |
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| Abstract: | This paper studies the nonnegative-definite solution of the matrix equation AXA*=B over quaternion field. The following problems are solved: (1) The necessary and sufficient condition for the existence of the nonnegative-definite solution to the matrix equation AXA*=B; (2) If the equation AXA*=B is consistent, we give a representation of the general solution to AXA*=B and an additive decomposition of the solutions; (3) If X is an nonnegative-definite solution to AXA*=B, we give the formula for the rank of X and the conditions under which X is a maximal or minimal rank solution. |
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| Keywords: | quaternion field nonnegative-definite matrix positive-definite matrix full rank factorization 1-inverse |
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