**Reference:**

B. De Schutter and
B. De Moor,
"The QR decomposition and the singular value decomposition in the
symmetrized max-plus algebra," *SIAM Journal on Matrix Analysis and
Applications*, vol. 19, no. 2, pp. 378-406, Apr. 1998.

**Abstract:**

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, the
Hessenberg decomposition, the LU decomposition and so on.

Online version of the paper

Corresponding technical report: pdf file (342 KB)

@article{DeSDeM:96-24,

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},

journal={SIAM Journal on Matrix Analysis and Applications},

volume={19},

number={2},

pages={378--406},

month=apr,

year={1998},

doi={10.1137/S0895479896304782}

}

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