Displaying similar documents to “A sharpening of the Parikh mapping”

A sharpening of the Parikh mapping

Alexandru Mateescu, Arto Salomaa, Kai Salomaa, Sheng Yu (2010)

RAIRO - Theoretical Informatics and Applications

Similarity:

In this paper we introduce a sharpening of the Parikh mapping and investigate its basic properties. The new mapping is based on square matrices of a certain form. The classical Parikh vector appears in such a matrix as the second diagonal. However, the matrix product gives more information about a word than the Parikh vector. We characterize the matrix products and establish also an interesting interconnection between mirror images of words and inverses of .

Intervals of certain classes of Z-matrices

M. Rajesh Kannan, K.C. Sivakumar (2014)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.