| 刘晓冀,张苗,BENITEZ Julio.$k$-次幂等矩阵线性组合群逆和超广义幂等矩阵线性组合Moore-Penrose广义逆的表[J].数学年刊A辑,2014,35(4):463~478 |
| $k$-次幂等矩阵线性组合群逆和超广义幂等矩阵线性组合Moore-Penrose广义逆的表 |
| Expressions of the Group Inverse of the Linear Combinations of k-Idempotent Matricesand the Moore-Penrose Generalized Inverse of the Linear Combinations of theHypergeneralized Idempotent Matrices |
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| DOI： |
| 中文关键词: 线性组合, 立方幂等矩阵, $k$-次幂等矩阵, 超广义幂等矩阵 |
| 英文关键词:Linear combinations, Tripotent matrices,
$k$-Idempotent matrices, Hypergeneralized idempotent matrices |
| 基金项目:国家自然科学基金 (No.11361009), 广西省自然科学基金(No.2013GXNSFAA019008), 广西教育厅重点项目(No.201202ZD031)
和瓦伦西亚理工大学科研项目(No.SP20120474, No.SP20120498) |
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| 中文摘要: |
| 在 $T_{1}T_{2}T_{1}=T_{2}$, $T_{2}T_{1}^{k-1}=T_{1}T_{2}^{k-1}$ 和 $T_{1}T_{2}T_{1}=T_{2}T_{1}$的条件下, 得到k-次幂等矩阵线性组合群逆的表示.
另外, 在$T_{1}T_{2}T_{1}=T_{2}$ 和 $T_{1}^{2}T_{2}=T_{2}$ 的条件下, 计算超广义幂等矩阵线性组合Moore-Penrose 广义逆的表示 |
| 英文摘要: |
| In this paper, the expressions of the group inverse of the linear
combinations of $k$-idempotent matrices under the conditions
$T_{1}T_{2}T_{1}=T_{2}$, $T_{2}T_{1}^{k-1}=T_{1}T_{2}^{k-1}$ and
$T_{1}T_{2}T_{1}=T_{2}T_{1}$ are given. Moreover. The authors investigate the
expressions of the Moore-Penrose generalized inverse of the
linear combinations of the hypergeneralized idempotent matrices under
the conditions $T_1T_2T_1=T_2$ and $T^2_1T_2=T_2$. |
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