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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