LIP6 1998/050

• Reports «Propriétés combinatoires des matrices sur les (pré)-semi-anneaux»
• M. Minoux
• 45 pages - 12/31/1998 - document en - http://www.lip6.fr/lip6/reports/1998/lip6.1998.050.ps.gz 103 Ko
• Contact Michel.Minoux (at) nulllip6.fr
• Ancien Thème : ANP
Many classical properties of real matrices actually derive from purely combinatorial properties which remain valid in algebraic structures much more general than the field of real numbers, namely semi-rings and pre-semi-rings. We present here generalizations to semi-rings of : - the CAYLEY-HAMILTON Theorem ; - the so-called "Matrix Tree Theorem" due to BORCHARDT and TUTTE, and its extended version, the "All Minors Matrix Tree Theorem". - the MACMAHON "Master Theorem".