The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

We show that several decision problems originating from max-plus or tropical convexity are
equivalent to zero-sum two player game problems. In particular, we set up an equivalence …

We investigate different notions of linear independence and of matrix rank that are relevant
for max-plus or tropical semirings. The factor rank and tropical rank have already received …

This survey presents an overview of the advances around Tverberg's theorem, focusing on
the last two decades. We discuss the topological, linear-algebraic, and combinatorial …

We give a characterization of the minimal tropical half-spaces containing a given tropical
polyhedron, from which we derive a counter-example showing that the number of such …

We establish a characterization of the vertices of a tropical polyhedron defined as the
intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a …

A combinatorial simplex algorithm is an instance of the simplex method in which the pivoting
depends on certain combinatorial data only. We show that any algorithm of this kind admits …

We extend the fundamentals for tropical convexity beyond the tropically positive orthant
expanding the theory developed by Loho and V\'egh (ITCS 2020). We study two notions of …

The celebrated upper bound theorem of McMullen determines the maximal number of
extreme points of a polyhedron in terms of its dimension and the number of constraints …

We study the max-plus or tropical analogue of the notion of polar: the polar of a cone
represents the set of linear inequalities satisfied by its elements. We establish an analogue …