Characterizations and perturbation analysis of a class of matrices related to core-EP inverses

Abstract Let A , B ∈ ℂ n × n with ind ( A ) = k and ind ( B ) = s and let L B = B 2 B † ○ . A new condition ( C s , ∗ ) : R ( A k ) ∩ N ( ( B s ) ∗ ) = { 0 } and R ( B s ) ∩ N ( ( A k ) ∗ ) = { 0 } , is defined. Some new characterizations related to core-EP inverses are obtained when B satisfies condition ( C s , ∗ ) . Explicit expressions of B † ○ and B B † ○ are also given. In addition, equivalent conditions, which guarantee that B satisfies condition ( C s , ∗ ) , are investigated. We proved that B satisfies condition ( C s , ∗ ) if and only if L B has a fixed matrix form. As an application, upper bounds for the errors ∥ B † ○ − A † ○ ∥ ∕ ∥ A † ○ ∥ and ∥ B B † ○ − A A † ○ ∥ are studied.