| 类幂等矩阵及其若干性质的研究 |
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| 引用本文： | 申士海,冀珂,董肖凯,秦波,赵良.类幂等矩阵及其若干性质的研究[J].安徽工业大学学报,2014(1):103-106. |
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| 作者姓名： | 申士海 冀珂 董肖凯 秦波 赵良 |
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| 作者单位： | 安徽工业大学数理学院,安徽马鞍山243032 |
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| 基金项目： | 安徽省高校自然科学研究项目（KJ2012Z028）;安徽工业大学SRTP项目（2012076） |
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| 摘 要： | 定义满足条件A2=BA的矩阵A为B-类幂等矩阵,研究幂等矩阵的一种推广形式。给出复数域上类幂等矩阵可对角化的条件,对如何将复数域中任一矩阵分解为类幂等矩阵进行研究。同时研究类幂等矩阵的若当分解和秩不等式,给出类幂等矩阵秩之间的大小关系和若当分解的形式,推广了矩阵理论中关于幂等矩阵的一些研究结果。
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| 关 键 词： | 类幂等矩阵 幂等矩阵 可逆矩阵 |
Studies of Similar Idempotent Matrix and its Properties |
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| SHEN Shihai,JI Ke,DONG Xiaokai,QING Bo,ZHAO Liang.Studies of Similar Idempotent Matrix and its Properties[J].Journal of Anhui University of Technology,2014(1):103-106. |
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| Authors: | SHEN Shihai JI Ke DONG Xiaokai QING Bo ZHAO Liang |
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| Affiliation: | (School of Mathematics ＆ Physics, Anhui University of Technology, Ma＇anshan 243032, China) |
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| Abstract: | By defing matrix A as B-similar idempotent if it satisfies the condition of A2= BA, a generalization of idempotent matrix was investigated. The conditions of diagonalization of similar idempotent matrices on complex field was characterized, and the method on how to decompose a matrix on complex field into similar idempotent matrices was discussed. Moreover, the Jordan form and the rank of similar idempotent matrices was studied, and some inequalities of matrix rank as well as the forms of Jordan decompositions of similar idempotent matrices were obtained. As a result, some well-known results on idempotent matrix in matrix theory were generalized. |
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| Keywords: | similar idempotent matrix idempotent matrix invertible matrix |
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