A New Simultaneous Decomposition of a Matrix Quaternity Over an Arbitrary Division Ring with Applications

In this article, we give a new simultaneous decomposition concerning the general matrix quaternity over an arbitrary division ring ℱ. A practical algorithm for the decomposition of the matrix quaternity is also presented. As applications, we establish some necessary and sufficient conditions for the existence of the general solutions to the systems of matrix equations and over ℱ. In addition, we give the expressions of the general solutions to the systems when the solvability conditions are satisfied. Numerical examples are also given to illustrate the results of this article. Moreover, we mention that the findings of this article extend the some known results in the literature.

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