Semigroups of non-negative integral matrices

Entropy Reduction, Ordering in Sequence Spaces, and Semigroups of Non-negative Matrices

We develop a mathematical framework to investigate classiication or ordering of sequential input by means of nite-state algorithms, where the aim is to reduce the \diversity" at the output, that is, to achieve entropy reduction. Our main interest is in optimal time-varying strategies; here, given a ((nite) collection of algorithms sharing a common set of internal states, we consider ordering st...

Bounded Semigroups of Matrices

In this note are proved two conjectures of Daubechies and Lagarias. The first asserts that if Z is a bounded set of matrices such that all left infinite products converge, then 8 generates a bounded semigroup. The second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices. One definition involves the conventional spectral radius, and one involves t...

On Non-negative-valued Matrices.

cording to our Theorem, if (4) is fulfilled, f3 and a can be so chosen that (2) be fulfilled. This form shows, however, that the lowest term in the determinant Ioua'+ Owa-11, if considered as a polynomial in E, is {nT Hence, the lowest term in the determinant :u ± EWI is I0K-1Iaean-r, i.e., the coefficient of (n7r in the determinant |u + Ew| does not vanish. Conversely, let us assume that u and...

On Clans of Non-negative Matrices

A clan is a compact connected topological semigroup with identity. Professor A. D. Wallace has raised the following question [9]: Is a clan of real »X» matrices with non-negative entries, which contains the identity matrix, necessarily acyclic? That is to say, do all of the Alexander-Cech cohomology groups with arbitrary coefficients (in positive dimensions) vanish? In this paper the slightly s...

Contractive inhomogeneous products of non - negative matrices