Codes and noncommutative stochastic matrices

Sylvain Lavallée (1) , Christophe Reutenauer (2) , Vladimir Retakh (3) , Dominique Perrin (4)

1 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
2 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]
3 Department of Mathematics - Rutgers School of Arts and Sciences
4 LIGM - Laboratoire d'Informatique Gaspard-Monge

Given a matrix over a skew field fixing the column ^t(1,...,1), we give formulas for a row vector fixed by this matrix. The same techniques are applied to give noncommutative extensions of probabilistic properties of codes.

Mots clés: stochastic matrices; codes; eigenvectors; quasi-determinants

Domaines: Théorie et langage formel [cs.FL]

Sylvain Lavallée, Christophe Reutenauer, Vladimir Retakh, Dominique Perrin. Codes and noncommutative stochastic matrices. Journal of Noncommutative Geometry, 2010, 4 (4), pp.531-554. ⟨10.4171/JNCG/65⟩. ⟨hal-00793906⟩