On the Infinite Products of Matrices

Yousry S.  Hanna; Samya F.  Ragheb

doi:10.4236/apm.2012.25050

Yousry S. Hanna^*, Samya F. Ragheb

Abstract: In different fields in space researches, Scientists are in need to deal with the product of matrices. In this paper, we develop conditions under which a product Пi=0∞ of matrices chosen from a possibly infinite set of matrices M={Pj, j∈J} converges. There exists a vector norm such that all matrices in M are no expansive with respect to this norm and also a subsequence {ik}k=0∞ of the sequence of nonnegative integers such that the corresponding sequence of operators {Pik}k=0∞ converges to an operator which is paracontracting with respect to this norm. The continuity of the limit of the product of matrices as a function of the sequences {ik}k=0∞ is deduced. The results are applied to the convergence of inner-outer iteration schemes for solving singular consistent linear systems of equations, where the outer splitting is regular and the inner splitting is weak regular.

Keywords: Matrices; Infinite Products; Iteration

Cite this paper: Y. Hanna and S. Ragheb, "On the Infinite Products of Matrices," Advances in Pure Mathematics, Vol. 2 No. 5, 2012, pp. 349-353. doi: 10.4236/apm.2012.25050.

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