In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.

The max-plus semiring Rmax is the set R∪{−∞}, equipped with the addition (a, b) 7→ max(a, b) and the multiplication (a, b) 7→ a + b. The identity element for the addition, zero, is −∞, and the identity element for the multiplication, unit, is 0. To illuminate the linear algebraic nature of the results, the generic notations +, , × (or concatenation), 0 and 1 are used for the addition, the sum, ...

In this paper circulant matrices in max-plus algebra are presented. Circulant matrices are special form of matrices which are entered by vector of inputs. For special types of matrices such as circulant matrices, the computation can often be performed in the simpler way than in the general case. The so-called max-plus algebra is useful for investigation of discrete events systems and the sequen...

This paper is an updated and extended version of the paper “The QR decomposition and the singular value decomposition in the symmetrized max-plus algebra” (by B. De Schutter and B. De Moor, SIAM Journal on Matrix Analysis and Applications, vol. 19, no. 2, pp. 378–406, April 1998). The max-plus algebra, which has maximization and addition as its basic operations, can be used to describe and anal...

The max-plus algebra has maximization and addition as basic operations, and can be used to model a certain class of discrete event systems. In contrast to linear algebra and linear system theory many fundamental problems in the max-plus algebra and in max-plus-algebraic system theory still need to be solved. In this paper we discuss max-plus-algebraic analogues of some basic matrix decompositio...

We provide an introduction to the max-plus algebra and explain how it can be used to model a specific class of discrete event systems with synchronization but no concurrency. Such systems are called max-plus linear discrete event systems because they can be described by a model that is “linear” in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how thes...

In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...

In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...

In this paper we prove a new characterization of the max-plus singular values of a maxplus matrix, as the max-plus eigenvalues of an associated max-plus matrix pencil. This new characterization allows us to compute max-plus singular values quickly and accurately. As well as capturing the asymptotic behavior of the singular values of classical matrices whose entries are exponentially parameteriz...