When does rank(ABC) = rank(AB) + rank(BC) - rank(B) hold?
Yongge Tian, George P. H. Styan · International Journal of Mathematical Education in Science and Technology · 2002
The well-known Frobenius rank inequality established by Frobenius in 1911 states that the rank of the product ABC of three matrices satisfies the inequality rank(ABC) U rank(AB) + rank(BC)- rank(B) A new necessary and sufficient condition for equality to hold is presented and then some interesting consequences and applications are discussed.