References
- T. Ando. Generalized schur complement. Linear Algebra Appl., 27 (1979), pp. 173–186. doi: 10.1016/0024-3795(79)90040-5
- A. Ben-Iserael and T. N. E. Greville. Generalized Inverses: Theorey and Applications. Wiley-Interscience, 1974; 2nd Edition, Springer-Verlag, New York, 2002.
- R. E. Cline. Representations of the generalized inverse of sums of matrices. SIAM.J.Numer.Anal., 2 (1965), pp. 99–114.
- R. J. Duffin, D. Hazony and N. Morrison. Network synthesis through hybrid matrices. SIAM J.Appl.Math., 14 (1966), pp. 390–413. doi: 10.1137/0114032
- K. E. Erickson. A new operation for analyzing series parallel networks. IEEE Trans. Circuit Theory CT-6(1959), pp. 124–126. doi: 10.1109/TCT.1959.1086519
- J. A. Fill and D. E. Fishkind. The Moore-Penrose generalized inverse for sums of matrices. SIAM J. Matrix.Anal & Appl., 21 (2000), pp. 629–635. doi: 10.1137/S0895479897329692
- G. H. Golub and C. F. Van Loan. Matrix computations. third ed, Johns, Hopkins University Press, Baltimore, 1996.
- M. Gulliksson, X. Jin and Y. Wei. Perturbation bounds for constrained and weighted least squares problems. Linear Algebra Appl., 349 (2002), pp. 221–232. doi: 10.1016/S0024-3795(02)00262-8
- R. E. Hartwig. Rank factorization and Moore-Penrose inversion. J. Ind. Math. Soc., 26 (1976), pp. 49–63.
- K. Jbilou and A. Messaondi. Matrix recursive interpolation algorithm for block linear systems Direct methods. Linear Algebra Appl., 294 (1999), pp. 137–154. doi: 10.1016/S0024-3795(99)00056-7
- J. Z. Liu and F. Z. Zhang. Disc separation of the schur complement of diagonally dominant matrices and determinantal bounds. SIAM J. matrix. Anal. Appl., 27 (3) (2005), pp. 665–674. doi: 10.1137/040620369
- C. D. Meyer. Generalized inversion of modified matrices. SIAM J.Appl.Math., 24 (1973), pp. 315–323. doi: 10.1137/0124033
- G. Marsaglia and G. P. H. Styan. Equalities and inequalities for ranks of matrices. Linear Multilinear Algebra, 2 (1974), pp. 269–292. doi: 10.1080/03081087408817070
- S. K. Mitra and P. Bhimasankaram. Generalized inverse of partitioned matrices and recalculation of least squares estimates for data or model changes. Sankhya Ser. A., 33 (1971), pp. 395–410.
- N. Minamide. An extension of the matrix inversion lemma. SIAM J. Algebra. Discrete. Math., 6 (1985), pp. 371–377. doi: 10.1137/0606038
- D. V. Ouellette. Schur complements and statistics. Linear Algebra Appl., 36 (1981), pp. 187–295. doi: 10.1016/0024-3795(81)90232-9
- R. Penrose. A genaralized inverse for matrices. Proc. Cambridge Philos. Soc., 52 (1955), pp. 406–413. doi: 10.1017/S0305004100030401
- K. Radoslaw and K. Krezsztof. Generalized inverses of a sum of matrices. Sankhya Ser.A., 56 (1994), pp. 458–464.
- Y. Tian. Reverse order laws for generalized inverse of multiple matrix products. Linear Algebra Appl., 211 (1994), pp. 85–100. doi: 10.1016/0024-3795(94)90084-1
- Y. Tian. Upper and lower bounds for ranks of matrix expression using generalized inverses. Linear Algebra Appl., 355 (2002), pp. 187–214. doi: 10.1016/S0024-3795(02)00345-2
- G. Wang, Y. Wei and S. Qiao. Generalized Inverses: Theory and Computations. Science Press, Beijing, 2004.
- Y. Wei. The weighted Moore-Penrose inverse of modified matrices. Appl. Math. Comput., 122 (2001), pp. 1–13.
- Z. P. Xiong, Y. Y. Qin and S. F. Yuan. The maximal and minimal ranks of matrix expression with applications. Journal of Inequalities and Applications 2012, 2012: 54. doi: 10.1186/1029-242X-2012-54
- Z. P. Xiong, Y. Y. Qin and B. Zheng. The least square g-inverse for sum of matrices. Linear and Multilinear Algebra, 61 (2013), pp. 448–462. doi: 10.1080/03081087.2012.689985