| 数量幂等矩阵的秩等式的进一步研究 |
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| 引用本文： | 冯晓霞,陈梅香,晏瑜敏,黄少武,杨忠鹏.数量幂等矩阵的秩等式的进一步研究[J].吉林林学院学报,2012(2):141-148. |
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| 作者姓名： | 冯晓霞 陈梅香 晏瑜敏 黄少武 杨忠鹏 |
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| 作者单位： | [1]漳州师范学院数学系,福建漳州363000 [2]福建省高校重点实验室--莆田学院应用数学实验室,福建莆田351100 [3]莆田学院数学系,福建莆田351100 [4]广西民族大学数学与计算机学院,广西南宁530006 |
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| 基金项目： | 基金项目：福建省自然科学基金项目（2010J01018）;2008年福建省高校服务海西建设重点项目（2008HX03）;福建省教育厅科研基金项目（JA08196）;莆田学院教改项目（JG201018）. |
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| 摘 要： | 当存在非零数λ与μ使P2=λP，Q2=μQ时，称P，Q都是数量幂等矩阵．数量λ，μ对数量幂等矩阵P，Q起到基本的确定作用．从寻找与数量A，肛无关的数量幂等矩阵P，Q的运算的秩等式出发，得到了与λ，μ的“大小”无关的数量幂等矩阵P，Q的和、差、换位子和Jordan积的秩等式，所得结论是已有结果的有益拓展．
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| 关 键 词： | 幂等矩阵 数量幂等矩阵 秩等式 换位子 Jordan积 |
Further Researches on Rank Equalities of Scalar -potent Matrix |
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| Authors: | FENG Xiao-xia CHEN Mei-xiang YAN Yu-min HUANG Shao-wu YANG Zhong-peng |
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| Institution: | 1. Department of Mathematics ,Zhangzhou Normal University,Zhangzhou 363000, China ; 2. Applied Mathematics Laboratory of Putian University Key Laboratory in Universities of Fujian Province, Putian 351100, China; 3. Department of Mathematics, Putian University, Putian 351100, China ; 4. College of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, China) |
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| Abstract: | If there exist nonzero numbers λ and μ,such that p2 = λp,Q2 =μQ＇ then P and Q are said to be scalar-potent matrices, where the scalars λ and μ play a basic role. Started from searching the rank equality of the operation of scalar-potent matrices independently of the scalars λ and μ, we obtain the ones for the sum, difference, commutator and Jordan product of scalar-potent matrices P and Q, regardless of the size of λ ,μ. These results are useful expand for given results. |
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| Keywords: | idempotent matrix scalar-potent matrix rank equality commutator Jordan product |
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