Geodesic
The Jordan forms of $AB$ and $BA$
The electronic journal of linear algebra, Tome 18 (2009), pp. 281-288.

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

Summary: The relationship between the Jordan forms of the matrix products AB and BA for some given A and B was first described by Harley Flanders in 1951. Their non-zero eigenvalues and non-singular Jordan structures are the same, but their singular Jordan block sizes can differ by 1. We present an elementary proof that owes its simplicity to a novel use of the Weyr characteristic.
Classification : 15A21, 15A18
Keywords: Jordan form, Weyr characteristic, eigenvalues 
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     title = {The {Jordan} forms of $AB$ and $BA$},
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Lippert, Ross A.; Strang, Gilbert. The Jordan forms of $AB$ and $BA$. The electronic journal of linear algebra, Tome 18 (2009), pp. 281-288. http://geodesic.mathdoc.fr/item/ELA_2009__18__a33/