| 矩阵广义逆的推广 |
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| 引用本文： | 罗自炎,修乃华.矩阵广义逆的推广[J].北方交通大学学报,2009(3):116-120. |
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| 作者姓名： | 罗自炎 修乃华 |
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| 作者单位： | 北京交通大学理学院,北京100044 |
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| 基金项目： | 基金项目：国家自然科学基金资助项目（10671010）;高等学校博士点基金项目资助（200800040024） |
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| 摘 要： | 广义逆矩阵在处理线性方程组与奇异值问题中的强大能力，使得这一理论得到广泛应用．本文将矩阵的广义逆推广到欧几里德若当代数中．首先，引入并刻画了欧几里德若当代数中元素的广义逆．然后，对该代数中一类重要的线性变换：Lyapunov变换的广义逆进行了刻画．最后，指出了欧几里德若当代数中广义逆理论的某些潜在应用．
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| 关 键 词： | 欧几里德若当代数 广义逆 Lyapunov变换 Lyapunov方程 |
Extensions for Generalized Inverse of Matrices |
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| LUO Ziyan,XIU Naihua.Extensions for Generalized Inverse of Matrices[J].Journal of Northern Jiaotong University,2009(3):116-120. |
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| Authors: | LUO Ziyan XIU Naihua |
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| Institution: | (School of Science, Beijing Jiaotong University, Beijing 100044, China) |
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| Abstract: | The theory of generalized inverse of matrices has been extensively studied due to its powerful capability of solving linear equations system and singular value problems. In this paper, we extend the generalized inverse of matrices to the setting of Euclidean Jordan algebra. We first introduce and characterize the concept of generalized inverse of the element in Euclidean Jordan algebra. We then introduce and characterize the concept of generalized inverse of Lyapunov transformation in Euclidean Jordan algebra. Finally, we indicate some potential applications for the theory of generalized inverse in Euclidean Jordan algebra. |
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| Keywords: | Euclidean Jordan algebra generalized inverse Lyapunov transformation Lyapunov equation |
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