MAXIMAL COLUMN RANKS AND THEIR PRESERVERS OF MATRICES OVER MAX ALGEBRA

Eigenvectors of interval matrices over max-plus algebra

The behaviour of a discrete event dynamic system is often conveniently described using a matrix algebra with operations max and plus Such a system moves forward in regular steps of length equal to the eigenvalue of the system matrix if it is set to operation at time instants corresponding to one of its eigenvectors However due to imprecise measurements it is often unappropriate to use exact mat...

On Some Properties of the Max Algebra System Over Tensors

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

Max-min ranks of products of two matrices and their generalized inverses

The present author recently established (J. Inequal. Appl., DOI: 10.1186/s13660016-1123-z) a group of exact formulas for calculating the maximum and minimum ranks of the products BA, and derived many algebraic properties of BA from the formulas, where A and B are two complex matrices such that the product AB is defined, and A and B are the {i, . . . , j}-inverses of A and B, respectively. As a ...

Nonnegative matrices, max-algebra and applications

Preservers of term ranks and star cover numbers of symmetric matrices

Let Sn(S) denote the set of symmetric matrices over some semiring, S. A line of A ∈ Sn(S) is a row or a column of A. A star of A is the submatrix of A consisting of a row and the corresponding column of A. The term rank of A is the minimum number of lines that contain all the nonzero entries of A. The star cover number is the minimum number of stars that contain all the nonzero entries of A. Th...