**Reference:**

B. De Schutter and
B. De Moor,
"The QR decomposition and the singular value decomposition in the
symmetrized max-plus algebra," *Proceedings of the European Control
Conference (ECC'97)*, Brussels, Belgium, 6 pp., July 1997. Paper
295/TH-E K6.

**Abstract:**

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 decompositions from
linear algebra that play an important role in linear system theory. We
use algorithms from linear algebra to prove the existence of
max-plus-algebraic analogues of the QR decomposition and the singular
value decomposition.

Corresponding technical report: pdf file (149 KB)

@inproceedings{DeSDeM:96-70,

author={B. {D}e Schutter and B. {D}e Moor},

title={The {QR} decomposition and the singular value decomposition in the symmetrized max-plus algebra},

booktitle={Proceedings of the European Control Conference (ECC'97)},

address={Brussels, Belgium},

month=jul,

year={1997},

note={Paper 295\,/\,TH-E K6}

}

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