### Group inverse for the block matrix with two identical subblocks over skew fields.

Zhao, Jiemei, Bu, Changjiang (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Zhao, Jiemei, Bu, Changjiang (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Catral, Minerva, Olesky, Dale D., van den Driessche, Pauline (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Bapat, R.B., Zheng, Bing (2003)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Beasley, LeRoy B. (1999)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Cantó, Rafael, Ricarte, Beatriz, Urbano, Ana M. (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that $$\text{rank}\left({P}^{*}AQ\right)=\text{rank}\left({P}^{*}A\right)+\text{rank}\left(AQ\right)-\text{rank}\left(A\right),$$ 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.

Bapat, R.B. (2007)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Tian, Yongge (2005)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Glebsky, Lev, Rivera, Luis Manuel (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Stanimirović, P. (1996)

Matematichki Vesnik

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Boston, Nigel (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Jeremy Lovejoy, Robert Osburn (2010)

Acta Arithmetica

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