**Finite iterative algorithms for a common solution to a group of complex matrix equations** |

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**Authors:** | Ai-Guo Wu Lingling LvMing-Zhe Hou |

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**Institution:** | ^{a} Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China
^{b} Institute of Electric Power, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, PR China
^{c} Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China |

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**Abstract:** | An iterative algorithm is constructed to give a common solution to a group of complex matrix equations. By using the proposed algorithm, the existence of a common solution can be determined automatically. When a common solution exists for this group of matrix equations, it is proven by using a real inner product in complex matrix spaces as a tool that a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a more general case. A numerical example is given to illustrate the effectiveness of the proposed method. |

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**Keywords:** | Finite iterative algorithm Complex matrix equation Inner product space Orthogonality Convergence property |

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