Abstract

In this paper, we introduce one type of matrix, called the weak group-star matrix. We investigate the characterizations, representations, and properties of the matrix. A variant of the successive matrix squaring computational iterative scheme is given for calculating the weak group-star matrix. Moreover, the Cramer?s rule for the solution of a singular equation (A?)*x = b is presented. Then, the perturbation is also given for the weak group-star matrix. In the final, the weak group-star matrix being used in solving appropriate systems of linear equations is established.

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