Frobenius inequality

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

References

1 Carl D. Meyer Matrix Analysis and Applied Linear Algebra

Title	Frobenius inequality
Canonical name	FrobeniusInequality
Date of creation	2013-03-22 15:30:03
Last modified on	2013-03-22 15:30:03
Owner	georgiosl (7242)
Last modified by	georgiosl (7242)
Numerical id	6
Author	georgiosl (7242)
Entry type	Theorem
Classification	msc 15-00