Rank equalities for block matrices and their Moore-Penrose inverses

Houston Journal of Mathematics

Volumn 30, Issue 2, 2004, Pages 483-510

  Tian, Yongge ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

Block matrix; Moore Penrose inverse; Outer inverse; Range; Rank

Indexed keywords

EID: 3042598385     PISSN: 03621588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. A. Ben-Israel, T. N. E. Greville, Generalized inverses: theory and applications. Corrected reprint of the 1974 original. Robert E. Krieger Publishing Co., Inc., Huntington, New York, 1980.
2. S. L. Campbell, C. D. Meyer, Jr., Generalized inverses of linear transformations, Corrected reprint of the 1979 original, Dover Publications, Inc., New York, 1991.
3. G. Marsaglia, G. P. H. Styan, Equalities and inequalities for ranks of matrices, Linear and Multilinear Algebra 2 (1974), 269-292.
4. G. Marsaglia, G. P. H. Styan, Rank conditions for generalized inverses of partitioned matrices, Sankhyā Ser. A 36 (1974), 437-442.
5. C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices and Its Applications, Wiley, New York, 1971.
6. R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406-413.
7. Y. Tian, The Moore-Penrose inverse of a triple matrix product, Math. Theory Practice 22(1), (1992), 64-70.
8. Y. Tian, Reverse order laws for the generalized inverses of multiple matrix products, Linear Algebra Appl. 211 (1994), 185-200.
9. Y. Tian, The Moore-Penrose inverses of m × n block matrices and their applications, Linear Algebra Appl. 283 (1998), 35-60.
10. Y. Tian, How to characterize equalities for a matrix and its Moore-Penrose inverse, Kyungpook Math. J. 41 (2001), 1-15.
11. Y. Tian, Rank equalities related to outer inverses of matrices and applications, Linear and Multilinear Algebra 49 (2002), 269-288.
12. Y.Tian, More on rank equalities for outer inverses of matrices with applications, Int. J. Math. Game Theory Algebra 12 (2002), 137-151.
13. Y. Tian, How to express a parallel sum of k matrices, J. Math. Anal. Appl. 266 (2002), 333-341.
14. Y. Tian, The maximal and minimal ranks of some expressions of generalized inverses of matrices, Southeast Asian Bull. Math. 25 (2002), 745-755.
15. Y. Tian, Upper and lower bounds for ranks of matrix expressions using generalized inverses, Linear Algebra and Appl. 355 (2002), 187-214.
16. Y. Tian, The minimal rank of the matrix expression A - BX - YC, Missouri J. Math. Sci. 14 (2002), 40-48.
17. S. Zlobec, An explicit form of the Moore-Penrose inverse of an arbitrary complex matrix, SIAM Review 12 (1970), 132-134.