Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings

Nonnegative matrices, max-algebra and applications

Max-algebra: the linear algebra of combinatorics?

Let a ⊕ b = max(a, b), a ⊗ b = a + b for a, b ∈ R := R ∪ {−∞}. By max-algebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗) extended to matrices and vectors. Max-algebra, which has been studied for more than 40 years, is an attractive way of describing a class of nonlinear problems appearing for instance in machinescheduling, information technology and ...

Simultaneous solution of linear equations and inequalities in max-algebra

Let a⊕b = max(a, b) and a⊗b = a+b for a, b ∈ R. Max-algebra is an analogue of linear algebra developed on the pair of operations (⊕,⊗) extended to matrices and vectors. The system of equations A ⊗ x = b and inequalities C ⊗ x ≤ d have each been studied in the literature. We consider a problem consisting of these two systems and present necessary and sufficient conditions for its solvability. We...

Linear systems in (max,+) algebra

Proceedings of the 29th Conference on Decision and Control Honolulu, Dec. 1990 Abstract In this paper, we study the general system of linear equations in the algebra. We introduce a symmetrization of this algebra and a new notion called balance which generalizes classical equations. This construction results in the linear closure of the algebra in the sense that every nondegenerate system of li...

Some results on Haar wavelets matrix through linear algebra

Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.