Rank equalities related to the generalized inverse with applications

Wang, Qingwen; Song, Guang-Jing; Lin, Chunyan

doi:10.1016/j.amc.2008.08.016

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Extremal Ranks Of (9) Subject To System (10)1

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Cited by 6 publications

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“…Now we simplify the ranks of block matrices in (25). In view of Lemma 2, block Gaussian elimination, (11), (12), and (23), we have the following: 0 0…”

Section: Extremal Ranks Of (9) Subject To System (10)mentioning

confidence: 99%

Ranks of a Constrained Hermitian Matrix Expression with Applications

2013

Journal of Applied Mathematics

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We establish the formulas of the maximal and minimal ranks of the quaternion Hermitian matrix expressionC4−A4XA4∗whereXis a Hermitian solution to quaternion matrix equationsA1X=C1,XB1=C2, andA3XA3*=C3. As applications, we give a new necessary and sufficient condition for the existence of Hermitian solution to the system of matrix equationsA1X=C1,XB1=C2,A3XA3*=C3, andA4XA4*=C4, which was investigated by Wang and Wu, 2010, by rank equalities. In addition, extremal ranks of the generalized Hermitian Schur complementC4−A4A3~A4∗with respect to a Hermitian g-inverseA3~ofA3, which is a common solution to quaternion matrix equationsA1X=C1andXB1=C2, are also considered.

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“…Now we simplify the ranks of block matrices in (25). In view of Lemma 2, block Gaussian elimination, (11), (12), and (23), we have the following: 0 0…”

Section: Extremal Ranks Of (9) Subject To System (10)mentioning

confidence: 99%