Some inequalities on generalized Schur complements

Linear Algebra and Its Applications

Volumn 302-303, Issue , 1999, Pages 163-172

  Wang, Bo Ying ^a   Zhang, Xiuping ^a   Zhang, Fuzhen ^b  

^a BEIJING NORMAL UNIVERSITY   (China)

^b NOVA SOUTHEASTERN UNIVERSITY   (United States)

Author keywords

Generalized inverse; Positive semidefinite matrix; Schur complement

Indexed keywords

EID: 0033269615     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00071-3     Document Type: Article

References (16)

1. A. Albert, Conditions for positive and nonnegative definiteness in terms of pseudoinverse, SIAM J. Appl. Math. 17 (1969) 434-440.
2. T. Ando, Generalized Schur complements, Linear Algebra Appl. 27 (1979) 173-186.
3. R.B. Bapat, A refinement of Oppenheim's inequality, in: F. Uhlig, R. Grone (Eds.), Current Trends in Matrix Theory: Proceedings of the Third Auburn Matrix Theory Conference, Auburn University, Auburn, Alabama, March 1986, North-Holland, New York, 1987, pp. 29-32.
4. C.A. Butler, T.D. Morley, Six generalized Schur complements, Linear Algebra Appl. 106 (1988) 259-269.
5. R.W. Cottle, Manifestations of the Schur complement, Linear Algebra Appl. 8 (1974) 189-211.
6. D. Carlson, E. Haynsworth, T. Markham, A generalization of the Schur complement by means of the Moore-Penrose inverse, SIAM J. Appl. Math. 26 (1974) 169-175.
7. E.V. Haynsworth, Determination of the inertia of a partitioned Hermitian matrix, Linear Algebra Appl. 1 (1968) 73-81.
8. E.V. Haynsworth, Reduction of a matrix using properties of the Schur complement, Linear Algebra Appl. 3 (1970) 23-29.
9. E.V. Haynsworth, Applications of an inequality for the Schur complement, Proc. Amer. Math. Soc. 24 (1970) 512-516.
10. R.A. Horn, C.R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985.
11. G.P.H. Styan, Schur complements and linear statistical models, in: S. Puntanen, T. Pukkila (Eds.), Proceedings of the First International Tampere Seminar on Linear Statistical Models and their Applications: Tampere, Finland, August-September 1983, Department of Mathematical Sciences, University of Tampere, 1985, pp. 37-75.
12. R. Smith, Some interlacing properties of the Schur complement of a Hermitian matrix, Linear Algebra Appl. 177 (1992) 137-144.
13. B.-Y. Wang, F. Zhang, SIAM J. of Matrix Analysis and Appl. 16 (4) (1995) 1173-1183.
14. B.-Y. Wang, F. Zhang, Schur complements and matrix inequalities of Hadamard products, Linear and Multilinear Algebra 43 (1997) 315-326.
15. F. Zhang, Linear Algebra: Challenging Problems for Students, Johns Hopkins University Press, Baltimore, 1996.
16. F. Zhang, Matrix Theory: Basic Results and Techniques, Springer, New York, 1999.