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Yongge Tian and Shizhen Cheng
The maximal and minimal ranks of A - BXC with applications
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| Published: |
December 7. 2003 |
| Keywords: |
Block matrix; generalized inverse; linear matrix expression; maximal rank; minimal rank; range; rank equation; Schur complement; shorted matrix. |
| Subject: |
15A03, 15A09. |
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Abstract
We consider how to take X such that the linear matrix expression
A - BXC attains its maximal and minimal ranks, respectively.
As applications, we investigate the rank invariance and the range
invariance of A - BXC with respect to the choice of X. In addition,
we also give the general solution of the rank equation
rank(A - BXC) + rank(BXC) = rank(A) and
then determine the minimal rank of A - BXC subject to this equation.
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| Author information
Yongge Tian:
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada K7L 3N6
ytian@mast.queensu.ca
Shizhen Cheng:
Department of Mathematics, Tianjin Polytechnic University, Tianjin, China 300160
csz@mail.tjpu.edu.cn
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