Geodesic
Eigenvalue multiplicities of products of companion matrices
The electronic journal of linear algebra, Tome 11 (2004), pp. 103-114.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: It is shown that under suitable conditions an eigenvalue of a product of companion matrices has geometric multiplicity equal to one. The result is used to show that for a class of Random Walks in Periodic Environments recurrence is equivalent to a product of companion matrices having 1 as an eigenvalue of algebraic multiplicity greater than one.
Classification : 15A18, 15A21, 60J10
Keywords: matrix products, eigenvalue multiplicities, companion matrices, random walk in a periodic environment 
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     author = {Key, Eric S. and Volkmer, Hans},
     title = {Eigenvalue multiplicities of products of companion matrices},
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     year = {2004},
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     url = {http://geodesic.mathdoc.fr/item/ELA_2004__11__a12/}
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Key, Eric S.; Volkmer, Hans. Eigenvalue multiplicities of products of companion matrices. The electronic journal of linear algebra, Tome 11 (2004), pp. 103-114. http://geodesic.mathdoc.fr/item/ELA_2004__11__a12/