On the Infinite Products of Matrices
Yousry S. Hanna, Samya Felobos Ragheb · Advances in Pure Mathematics · 2012
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.