The QR Decomposition and the Singular Value Decomposition in the Symmetrized Max-Plus Algebra
Bart De Schutter, Bart De Moor · SIAM Journal on Matrix Analysis and Applications · 1998
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 algorithms from linear algebra to prove the existence of max-algebraic analogues of the QR decomposition, the singular value decomposition (SVD), the Hessenberg decomposition, the LU decomposition, and so on.