The reverse order law for the generalized inverse A(2) T,S

Applied Mathematics and Computation

Volumn 157, Issue 2, 2004, Pages 295-305

  Wang, Guorong ^a   Zheng, Bing ^b  

^a SHANGHAI NORMAL UNIVERSITY   (China)

^b LANZHOU UNIVERSITY   (China)

Author keywords

Generalized inverse A(2)T,S; Matrix product; Reverse order law

Indexed keywords

GENERALIZED INVERSE A(2)T,S; MATRIX PRODUCT; REVERSE ORDER LAW;

INVERSE PROBLEMS; MARKOV PROCESSES; MATHEMATICAL MODELS; NUMBER THEORY; STATISTICAL METHODS;

MATRIX ALGEBRA;

EID: 4444251553     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.08.034     Document Type: Article

References (18)

1. Getson A.J., Hsuan F.C. {2}-Inverse and their Statistical Applications. Lecture Notes in Statistics. 47:1988;Springer, Berlin.
2. Hustn F., Langenberg P., Getson A. The {2}-inverse with applications to statistics. Linear Algebra Appl. 70:1985;241-248.
3. Campbell S.L., Meyer C.D. Generalized Inverse of Linear Transformations. 1979;Pitman, London.
4. Greville T.N.E. Note on the generalized inverse of a matrix product. SIAM Rev. 8:1966;518-521.
5. Hartwig R.E. The reverse order law revisited. Linear Algebra Appl. 76:1986;241-246.
6. Tian Y. The Moore-Penrose inverse of a triple matrix product. (in Chinese) Math. Practice Theory. 1:1992;64-70.
7. Tian Y. Reverse order laws for the generalized inverse of multiple matrix products. Linear Algebra Appl. 211:1994;85-100.
8. Sun W., Wei Y. Inverse order rule for weighted generalized inverse. SIAM J. Matrix Anal. Appl. 19(3):1998;772-775.
9. Sun W., Wei Y. Triple reverse order law for weighted generalized inverse. Appl. Math. Comput. 125:2002;221-229.
10. Wang G., Gao J. Reverse order laws for the weighted Moore-Penrose inverse of a triple matrix product. (in Chinese) J. Shanghai Teachers Univ. 29(3):2000;1-8.
11. D J. Math. Res. Exposition. 19(2):1999;355-358.
12. Wang G. The reverse order law for the Drazin inverses of multiple matrix products. Linear Algebra Appl. 384:2002;265-272.
13. Wei M. Equivalent conditions for generalized inverses of products. Linear Algebra Appl. 266:1997;347-363.
14. De Pierro A.R., Wei M. Reverse order law for reflexive generalized inverses of products of matrices. Linear Algebra Appl. 277:1996;299-311.
15. Wei M. Reverse order laws for generalized inverse of multiple matrix products. Linear Algebra Appl. 293:1999;273-288.
16. Ben-Israel A., Greville T.N.E. Generalized Inverses: Theory and Applications. 1974;Wiely, New York.
17. Marsaglia G., Styan G.P. Equalities and inequalities for rank of matrices. Linear Multilinear Algebra. 2:1974;269-292.
18. Hartwig R.E. Block generalized inverse. Arch. Rational Mech. Anal. 61:1976;197-251.