ELA, Volume 13, pp. 249-261, November 2005, abstract.
Special Forms of Generalized Inverses of Row Block Matrices
Yongge Tian
Given a row block matrix [A, B], this paper investigates the relations
between the generalized inverse [A, B]^- and the column block matrix
[(A^-)^T (B^-)^T]^T consisting of two generalized inverses A^- and B^-.
The first step of the investigation is to establish a formula for the
minimal rank of the difference
[A, B\,]^- - [(A^-)^T (B^-)^T]^T,
the second step is to find a necessary and sufficient condition for
[A, B\,]^- = [(A^-)^T (B^-)^T]^T
to hold by letting the minimal rank be zero. Seven types of generalized
inverses of matrices are taken into account.