Nonnegative matrices and M-matrices have become a staple in contemporary linear
algebra, and they arise frequently in its applications. Such matrices are encountered not …

Ergodicity coefficients for stochastic matrices determine inclusion regions for subdominant
eigenvalues; estimate the sensitivity of the stationary distribution to changes in the matrix; …

We analyse the ergodic properties of quantum channels that are covariant with respect to
diagonal orthogonal transformations. We prove that the ergodic behaviour of a channel in …

The scrambling index of a primitive digraph D is the smallest positive integer k such that for
every pair of vertices u and v, there is a vertex w such that we can get to w from u and v in D …

A set of nonnegative matrices M={M_1,M_2,...,M_k\} is called primitive if there exist possibly
equal indices i_1,i_2,...,i_m such that M_i_1M_i_2⋯M_i_m is entrywise positive. The length …

For positive integers k and m, and a digraph D, the k-step m-competition graph Cmk (D) of D
has the same set of vertices as D and an edge between vertices x and y if and only if there …

From the background of a memoryless communication system, we introduce the definition of
the generalized scrambling indices for a primitive digraph, which are natural extensions of …

A nonnegative square matrix A is primitive if some power Ak> 0 (that is, Ak is entrywise
positive). The least such k is called the exponent of A. In [2], Akelbek and Kirkland defined …

The long term behaviour of a quantum channel under iterations (ie under repeated
applications of itself) yields a plethora of interesting properties. These include ergodicity …

In 2009, Akelbek and Kirkland introduced a useful parameter called the scrambling index of
a primitive digraph D, which is the smallest positive integer k such that for every pair of …