Related papers: Tropical tensor product and beyond
In this article, we introduce an exponential for tropical matrices and show that this series is essential for the analysis of certain kinds of stability in discrete event dynamic systems. A notion of a generalised eigenvector is introduced…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
We study linear maps preserving the higher numerical ranges of tensor product of matrices.
We study the combinatorial properties of 2-dimensional tropical complexes. In particular, we prove tropical analogues of the Hodge index theorem and Noether's formula. In addition, we introduce algebraic equivalence for divisors on tropical…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
In this paper, we present methods for solving a system of linear equations, $ AX=b $, over tropical semirings. To this end, if possible, we first reduce the order of the system through some row-column analysis, and obtain a new system with…
We introduce and study, for a process P delivering edges on the Cartesian product of the vertex sets of a given set of graphs, the P-product of these graphs, thereby generalizing many types of product graph. Analogous to the notion of a…
A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.
The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
We study idempotent analogs of topological tensor products in the sense of A. Grothendieck. The basic concepts and results are simulated on the algebraic level. This is one of a series of papers on idempotent functional analysis.
We define the tensor product of filtered $A_\infty$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
We propose a new operator defined between two tensors, the broadcast product. The broadcast product calculates the Hadamard product after duplicating elements to align the shapes of the two tensors. Complex tensor operations in libraries…
We introduce the notion of resultant of two planar curves in the tropical geometry framework. We prove that the tropicalization of the algebraic resultant can be used to compute the stable intersection of two tropical plane curves. It is…
This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…
The tensor t-product, introduced by Kilmer and Martin [26], is a powerful tool for the analysis of and computation with third-order tensors. This paper introduces eigentubes and eigenslices of third-order tensors under the t-product. The…
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization…
The goal of this paper is to introduce a construction of a vector bundle on a tropical variety. When the base is a tropical toric variety these tropicalize toric vector bundles, and are described by the data of a valuated matroid and some…
We derive integral formulas that simplify the Vector Spherical Tensor Product recently introduced by Xie et al., which generalizes the Gaunt tensor product to antisymmetric couplings. In particular, we obtain explicit closed-form…