Expressions of the Group Inverse of the Linear Combinations of k-Idempotent Matrices and the Moore-Penrose Generalized Inverse of the Linear Combinations of the Hypergeneralized Idempotent Matrices

LIU Xiaoji; ZHANG Miao; BENíTEZ Julio

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Expressions of the Group Inverse of the Linear Combinations of k-Idempotent Matrices and the Moore-Penrose Generalized Inverse of the Linear Combinations of the Hypergeneralized Idempotent Matrices

机译：k幂等矩阵的线性组合的组逆和超广义幂等矩阵的线性组合的Moore-Penrose广义逆的表达

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摘要

In this paper, the expressions of the group inverse of the linear combinations of kidempotent matrices under the conditions T1T2T1 = T2, T2T_1~(k-1) = T1T_2~(k-1) and T1T2T1 = T2T1 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 T1T2T1 = T2 and T1~2T2 = T2.

机译：给出了在T1T2T1 = T2，T2T_1〜（k-1）= T1T_2〜（k-1）和T1T2T1 = T2T1的条件下，幂等矩阵线性组合的群逆的表达式。此外。作者研究了在条件T1T2T1 = T2和T1〜2T2 = T2的条件下超广义幂等矩阵的线性组合的Moore-Penrose广义逆的表达。

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来源
《Chinese journal of contemporary mathematics》 |2014年第3期|共16页
作者
LIU Xiaoji; ZHANG Miao; BENíTEZ Julio;
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正文语种 eng
中图分类数学;
关键词
Linear combinations; Tripotent matrices; k-Idempotent matrices; Hypergeneralized idempotent matriccs;

机译：线性组合;三幂矩阵;k-等幂矩阵;超广义等幂矩阵;

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1. Expressions of the Group Inverse of the Linear Combinations of k-Idempotent Matrices and the Moore-Penrose Generalized Inverse of the Linear Combinations of the Hypergeneralized Idempotent Matrices [J] . LIU Xiaoji, ZHANG Miao, BENíTEZ Julio Chinese journal of contemporary mathematics . 2014,第3期

机译：k幂等矩阵的线性组合的组逆和超广义幂等矩阵的线性组合的Moore-Penrose广义逆的表达
2. Generalized Inverses of a Linear Combination of Moore-Penrose Hermitian Matrices [J] . Marina To#353, i#263, Milan Mi#353, Filomat . 2016,第11期

机译：Moore-Penrose Hermitian矩阵的线性组合的广义逆
3. Some results on the group inverse of the block matrix with a sub-block of linear combination or product combination of matrices over skew fields [J] . Bu C., Zhang K., Zhao J. Linear & Multilinear Algebra: An International Journal Publishing Articles, Reviews and Problems . 2010,第7a8期

机译：关于块矩阵与偏字段上矩阵的线性组合或乘积组合的子块的块逆的一些结果
4. Constitution of Linear Combinations of Idempotent Matrices and its Properties [C] . Liu Xingxiang 2012 Eighth International Conference on Computational Intelligence and Security. . 2012

机译：幂等矩阵的线性组合的构成及其性质
5. APPLICATIONS OF GENERALIZED INVERSE TO CIRCULANT MATRICES, INTERSECTION PROJECTIONS, AND LINEAR PROGRAMMING [D] . NGUYEN, TUNG MANH 1982

机译：广义逆在循环矩阵，相交投影和线性规划中的应用
6. SIMULTANEOUSLY SPARSE SOLUTIONS TO LINEAR INVERSE PROBLEMS WITH MULTIPLE SYSTEM MATRICES AND A SINGLE OBSERVATION VECTOR [O] . ADAM C. ZELINSKI, VIVEK K. GOYAL, ELFAR ADALSTEINSSON -1

机译：同时稀疏解决多个系统矩阵和单个观察向量的线性逆问题
7. Notes on the Moore-Penrose inverse of a linear combination of commuting generalized and hypergeneralized projectors [O] . Marina Tosic 2017

机译：关于通勤通用和高级化投影仪的线性组合的摩尔猪肉逆的注意事项
8. Nonlinear Optimization Involving Polynomial Matrices and Their Generalized Inverses [R] . Hill, R. R. 1988

机译：涉及多项式矩阵及其广义逆的非线性优化问题

Expressions of the Group Inverse of the Linear Combinations of k-Idempotent Matrices and the Moore-Penrose Generalized Inverse of the Linear Combinations of the Hypergeneralized Idempotent Matrices

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