| 广义三次矩阵及其性质 |
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| 引用本文： | 朱蕾,张冬梅,杨忠鹏. 广义三次矩阵及其性质[J]. 吉林大学学报(理学版), 2014, 52(2): 195-200 |
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| 作者姓名： | 朱蕾 张冬梅 杨忠鹏 |
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| 作者单位： | 1. 浙江工业大学 理学院, 杭州 310023; 2. 莆田学院 数学学院, 福建 莆田 351100 |
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| 基金项目： | 国家自然科学基金(批准号:61074039);福建省自然科学基金(批准号:2013J00102);福建省高校服务海西建设重点项目(批准号:2008HX03) |
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| 摘 要： | 基于广义二次矩阵的性质和研究方法给出广义三次矩阵的定义, 并证明了广义三次矩阵对幂、 逆及线性运算封闭, 且在某些条件下广义三次矩阵可表示为3个两两可交换且乘积为零的幂等矩阵的线性组合. 结果表明, 二次矩阵是广义三次矩阵的特例.
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| 关 键 词： | 广义三次矩阵 广义二次矩阵 幂 逆 线性组合 |
| 收稿时间： | 2013-05-06 |
Generalized Cubic Matrix and Its Properties |
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| ZHU Lei,ZHANG Dong mei,YANG Zhong peng. Generalized Cubic Matrix and Its Properties[J]. Journal of Jilin University: Sci Ed, 2014, 52(2): 195-200 |
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| Authors: | ZHU Lei ZHANG Dong mei YANG Zhong peng |
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| Affiliation: | 1. College of Science, Zhejiang University of Technology, Hangzhou 310023, China;2. Department of Mathematics, Putian University, Putian 351100, Fujian Province, China |
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| Abstract: | Based on the properties of generalized quadratic matrix and method used, the generalized cubic matrix was defined. It is proved that the generalized cubic matrix is closed for the power, the inverse and linear operation of the matrix. It is also pointed out that under some conditions, the generalized cubic matrix can be represented as the linear combination of three idempotent matrices which are commutative and the products are zero. The results show
that genteralized quadratic matrix is a special case of the generalized cubic matrix. |
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| Keywords: | generalized cubic matrix generalized quadratic matrix power inverse linear combination |
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