A new rank formula for idempotent matrices with applications

Tian, Yong Ge, and Styan, George P. H.. "A new rank formula for idempotent matrices with applications." Commentationes Mathematicae Universitatis Carolinae 43.2 (2002): 379-384. <http://eudml.org/doc/248988>.

@article{Tian2002,
abstract = {It is shown that \[ \text\{\rm rank\}(P^*AQ) = \text\{\rm rank\}(P^*A) + \text\{\rm rank\}(AQ) - \text\{\rm rank\}(A), \] where $A$ is idempotent, $[P,Q]$ has full row rank and $P^*Q = 0$. Some applications of the rank formula to generalized inverses of matrices are also presented.},
author = {Tian, Yong Ge, Styan, George P. H.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Drazin inverse; group inverse; idempotent matrix; inner inverse; rank; tripotent matrix; Drazin inverse; group inverse; idempotent matrix; inner inverse; rank; tripotent matrix},
language = {eng},
number = {2},
pages = {379-384},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A new rank formula for idempotent matrices with applications},
url = {http://eudml.org/doc/248988},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Tian, Yong Ge
AU - Styan, George P. H.
TI - A new rank formula for idempotent matrices with applications
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 379
EP - 384
AB - It is shown that \[ \text{\rm rank}(P^*AQ) = \text{\rm rank}(P^*A) + \text{\rm rank}(AQ) - \text{\rm rank}(A), \] where $A$ is idempotent, $[P,Q]$ has full row rank and $P^*Q = 0$. Some applications of the rank formula to generalized inverses of matrices are also presented.
LA - eng
KW - Drazin inverse; group inverse; idempotent matrix; inner inverse; rank; tripotent matrix; Drazin inverse; group inverse; idempotent matrix; inner inverse; rank; tripotent matrix
UR - http://eudml.org/doc/248988
ER -