Rank Inequalities over Semirings and their Linear Preservers
by
Alexander Guterman
Moscow State University

This talk is based on recent joint work with LeRoy B. Beasley.

Matrix theory over semirings is an object of intensive study during the recent years since it provides the interplay between the combinatorial matrix theory and theory of linear operators. The concept of matrix rank over semirings splits into several notions. Among them there are such classical functions as factor rank, term rank, zero-term rank, row and column ranks, etc.

In the present work we investigate the behavior of these semiring rank functions under the natural operations defined on matrix algebra. We establish the serious of upper and lower bounds which are exact and the best possible. The structure of matrix varieties which arise as extremal cases in these inequalities is far from being understood. However we give the complete characterization of bijective linear transformations on matrices that leave these varieties invariant.

Date received: December 21, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cake-10.