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Drazin inverse; group inverse; idempotent matrix; inner inverse; rank; tripotent matrix

References:

[1] Drury S.W., Liu S., Lu C.Y., Puntanen S., Styan G.P.H.: **Some comments on several matrix inequalities with applications to canonical correlations: historical background and recent developments**. Report A332 (December 2000), Dept. of Mathematics, Statistics and Philosophy, University of Tampere, Tampere, Finland, 63 pp. To be published in the special issue of {Sankhyā: The Indian Journal of Statistics, Series A} associated with ``An International Conference in Honor of Professor C.R. Rao on the Occasion of his 80th Birthday, Statistics: Reflections on the Past and Visions for the Future, The University of Texas at San Antonio, March 2000''.

[2] Tian Y.: **Two rank equalities associated with blocks of orthogonal projector. Problem $25$-$4$**. Image, The Bulletin of the International Linear Algebra Society 25 (2000), p.16 [Solutions by J.K. Baksalary & O.M. Baksalary, by H.J. Werner, and by S. Puntanen, G.P.H. Styan & Y. Tian, Image, The Bulletin of the International Linear Algebra Society 26 (2001), 6-9].

[3] Tian Y.: **Completing block matrices with maximal and minimal ranks**. Linear Algebra Appl. 321 (2000), 327-345. MR 1800003

[4] Tian Y., Styan, G.P.H.: **Some rank equalities for idempotent and involutory matrices**. Linear Algebra Appl. 335 (2001), 101-117. MR 1850817