Chapter 35
Max-Plus Algebra
Marianne Akian
INRIA and CMAP, École Polytechnique
Ravindra Bapat
Indian Statistical Institute
Stéphane Gaubert
INRIA and CMAP, École Polytechnique
Max-plus or tropical algebra has been discovered more or less independently by several schools, in relation with various mathematical fields. This chapter is limited to finite dimensional linear algebra. For more information, the reader may consult the books [CG79], [Zim81], [CKR84], [BCOQ92], [KM97], [GM02], [HOvdW05], and [But10]. The collections of articles [MS92], [Gun98], [LM05], and [LS09] give some idea of current developments. A number of recent results relevant to linear algebra have appeared in the field of tropical geometry, especially in relation with tropical ...
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