On infinite products of stochastic matrices

On the Infinite Products of Matrices

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  of matrices chosen from a possibly infinite set of matrices 0 i i P    , j  M P j J     k i P   0 k k i  converges. There exists a vector norm such that all matrices in M are no expansive with respect to this norm and also ...

Infinite products and paracontracting matrices

In [Linear Algebra Appl., 161:227{263, 1992] the LCP-property of a nite set of square complex matrices was introduced and studied. A set is an LCP-set if all left in nite products formed from matrices in are convergent. It was shown earlier in [Linear Algebra Appl., 130:65{82, 1990] that a set paracontracting with respect to a xed norm is an LCP-set. Here a converse statement is proved: If is a...

Correction to: On a decomposition for infinite stochastic matrices

Products of Stochastic Matrices and Applications

This paper deals with aspects of the limit behaviour of products of nonidentical finite or countable stochastic matrices (P). Applications n are given to nonhomogeneous Markov models as positive chains, some classes of finite chains considered by Doeblin and weakly ergodic chains.

Sets of Matrices All Infinite Products of Which Converge

An infinite product IIT= lMi of matrices converges (on the right) if limi __ M, . . . Mi exists. A set Z = (Ai: i > l} of n X n matrices is called an RCP set (rightconvergent product set) if all infinite products with each element drawn from Z converge. Such sets of matrices arise in constructing self-similar objects like von Koch’s snowflake curve, in various interpolation schemes, in construc...