Matrix operator equations

This article is devoted to the theory and applications of matrix operator equations in normed spaces. We describe in detail the general properties of matrix operators and their representing matrices. As the indexing set we take an arbitrary countable set. This is related to stochastic applications in which it is difficult to find an enumeration that fits well with the content. Sample applications are the Markov matrices and the operators they define. Comparisons with operators of this type arise in some stochastic problems of integral geometry and tomography.