| 可换对合阵组合的可逆性 |
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| 引用本文： | 陈引兰,左可正,谢涛.可换对合阵组合的可逆性[J].数学的实践与认识,2014(17). |
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| 作者姓名： | 陈引兰 左可正 谢涛 |
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| 作者单位： | 湖北师范学院数学与统计学院; |
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| 基金项目： | 湖北省教育厅重点项目(D20122202);湖北省教育厅青年项目(B20122203) |
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| 摘 要： | 先讨论两个可换对合阵P,Q线性组合aP+bQ可逆的充分必要条件及可逆时逆矩阵计算公式,再利用矩阵分解,以两种形式讨论两个可换对合阵P,Q组合aI+bP+cQ+dPQ及三个两两可换对合阵P,Q,R组合aI+bP+cQ+dPQ+eR+fPR+gQR+hPQR可逆的充分必要条件及可逆时分别给出逆矩阵计算公式.
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| 关 键 词： | 对合阵 逆矩阵 矩阵分解 矩阵的组合 |
On Nonsingularity of Combinations of Three Commuting Involutiory Matrices |
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| Abstract: | In this paper,necessary and sufficient conditions for nonsingularity of linear combinations aP + bQof two commuting involutiory matrices P,Qfirtly has been established,then necessary and sufficient conditions for nonsingularity of combinations aI + bP + cQ +dPQof two commuting involutiory matrices P,Qand combinations aI+bP+cQ+dPQ+eR+fPR + gQR + hPQR of three commuting involutiory matrices P,Q,R have been discussed by decomposition of matrices in two kinds of forms,the formulae of the inverse matrices also given respectively. |
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| Keywords: | involutiory matrices inverse matrices decomposition of matrices combinations of matrices |
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