Compactification of a set of matrices with convergent infinite products Original Research Article

We generalize and unify some aspects of the work of I. Daubechies, J.C. Lagarias [Linear Algebra Appl. 162 (1992) 227–263] on a set Σ of matrices with right-convergent-products (RCPs). We show that most properties of an RCP set Σ pass on to its compactification image (i.e., its closure in the matrix space). Results on finite RCP sets generally hold for compact RCP sets, among which is the existence of the König chain, an important tool for analyzing RCP sets.