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Frobenius inequality (Theorem)

For any matrices $ A$,$ B$,$ C$ such that $ ABC$ exists, then $ \operatorname{rank} AB + \operatorname{rank} BC \leq \operatorname{rank} ABC+ \operatorname{rank} B.$

Bibliography

1
Carl D. Meyer Matrix Analysis and Applied Linear Algebra



"Frobenius inequality" is owned by georgiosl.
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Cross-references: matrices
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This is version 3 of Frobenius inequality, born on 2005-09-06, modified 2005-09-07.
Object id is 7360, canonical name is FrobeniousInequality.
Accessed 1725 times total.

Classification:
AMS MSC: 15-00 (Linear and multilinear algebra; matrix theory :: General reference works )
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pretty proofs by matte on 2005-10-28 15:33:30
Proofs of this can be found here:

 http://www.artofproblemsolving.com/Forum/topic-33860.html

..hope we could have these kind of messages on PM someday too!
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