Necessary and sufficient conditions for the existence of the group inverse of the block matrix in Minkowski Space are studied, where are both square and . The representation of this group inverse and some related additive results are also given.
References
[1]
Zhuang, W. (1987) Involutory Functions and Generalized Inverses of Matrices over an Arbitrary Skew Fields. Northeast Math, 1, 57-65.
[2]
Golub, G.H. and Greif, C. (2003) On Solving Blocked-Structured Indefinite Linear Systems. SIAM Journal on Scientific Computing, 24, 2076-2092.
[3]
Ipsen, I.C.F. (2001) A Note on Preconditioning Nonsymmetric Matrices. SIAM Journal on Scientific Computing, 23, 1050-1051.
[4]
Campbell, S.L. and Meyer, C.D. (2013) Generalized Inverses of Linear Transformations. Dover, New York.
[5]
Bu, C. (2002) On Group Inverses of Block Matrices over Skew Fields. Journal of Mathematics, 35, 49-52.
[6]
Bu, C., Zhao, J. and Zheng, J. (2008) Group inverse for a Class 2 × 2 Block Matrices over Skew Fields. Computers & Mathematics with Applications, 204, 45-49. http://dx.doi.org/10.1016/j.amc.2008.05.145
[7]
Cao, C. (2001) Some Results of Group Inverses for Partitioned Matrices over Skew Fields. Heilongjiang Daxue Ziran Kexue Xuebao, 18, 5-7.
[8]
Cao, C. and Tang, X. (2006) Representations of the Group Inverse of Some 2 × 2 Block Matrices. International Mathematical Forum, 31, 1511-1517. http://dx.doi.org/10.12988/imf.2006.06127
[9]
Chen, X. and Hartwig, R.E. (1996) The Group Inverse of a Triangular Matrix. Linear Algebra and Its Applications, 237/238, 97-108. http://dx.doi.org/10.1016/0024-3795(95)00561-7
[10]
Catral, M., Olesky, D.D. and van den Driessche, P. (2008) Group Inverses of Matrices with Path Graphs. The Electronic Journal of Linear Algebra, 1, 219-233. http://dx.doi.org/10.13001/1081-3810.1260
[11]
Cao, C. (2006) Representation of the Group Inverse of Some 2 × 2 Block Matrices. International Mathematical Forum, 31, 1511-1517.
[12]
Krishnaswamy, D. and Punithavalli, G. (2013) The Anti-Reflexive Solutions of the Matrix Equation A × B=C in Minkowski Space M. International Journal of Research and Reviews in Applied Sciences, 15, 2-9.
[13]
Krishnaswamy, D. and Punithavalli, G. (2013) The Re-nnd Definite Solutions of the Matrix Equation A × B=C in Minkowski Space M. International Journal of Fuzzy Mathematical Archive, 2, 70-77.
[14]
Krishnaswamy, D. and Punithavalli, G. Positive Semidefinite (and Definite) M-Symmetric Matrices Using Schur Complement in Minkowski Space M. (Preprint)