On the Infinite Products of Matrices ()

Yousry S. Hanna, Samya F. Ragheb

Faculty of Science, Helwan University, Helwan, Egypt.

National Research Institute of Astronomy and Geophysics, Helwan, Egypt.

**DOI: **10.4236/apm.2012.25050
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Faculty of Science, Helwan University, Helwan, Egypt.

National Research Institute of Astronomy and Geophysics, Helwan, Egypt.

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 П_{i=0}^{∞} of matrices chosen from a possibly infinite set of matrices M={P_{j}, 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 {i_{k}}_{k=0}^{∞} of the sequence of nonnegative integers such that the corresponding sequence of operators {P_{ik}}_{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 {i_{k}}_{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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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