Linear operators that preserve zero-term rank over fields and rings

Linear operators that preserve some test functions

The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical approximation to approximation in abst...

Linear Systems over rings of operators

Linear Operators That Preserve Graphical Properties of Matrices: Isolation Numbers

Let A be a Boolean {0, 1} matrix. The isolation number of A is the maximum number of ones in A such that no two are in any row or any column (that is they are independent), and no two are in a 2 × 2 submatrix of all ones. The isolation number of A is a lower bound on the Boolean rank of A. A linear operator on the set of m× n Boolean matrices is a mapping which is additive and maps the zero mat...

Linear operators that strongly preserve graphical properties of matrices - II

Beasley, L.B. and N.J. Pullman, Linear operators that strongly preserve graphical properties of matrices, Discrete Mathematics 104 (1992) 143-157. An operator on the set Ju of n X n matrices strongly preserves a subset 9 if it maps 9 into 9 and A\% into A\%. The operator semigroup of 9 is the semigroup of linear operators strongly preserving 9. We show that all the n x n matrix-families which a...

Linear operators that strongly preserve regularity of fuzzy matrices

An n× n fuzzy matrix A is called regular if there is an n× n fuzzy matrix G such that AGA = A. We study the problem of characterizing those linear operators T on the fuzzy matrices such that T (X) is regular if and only if X is. Consequently, we obtain that T strongly preserves regularity of fuzzy matrices if and only if there are permutation matrices P and Q such that it has the form T (X) = P...