Inverse forms of Hadamard inequality

SIAM Journal on Matrix Analysis and Applications

Volumn 23, Issue 4, 2002, Pages 990-997

  Gangsong, Leng ^a   Guobiao, Zhou ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Canonical volume; Inequality; Inverse forms; Parallelotope

Indexed keywords

EID: 0036400779     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479801387279     Document Type: Article

References (16)

1. E.F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, 1961.
2. W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, Academic Press, New York, 1975.
3. J.D. Dixon, How good is Hadamard's inequality for determinants?, Canad. Math. Bull., 27 (1984), pp. 260-264.
4. J.D. Dixon, Estimating extremal eigenvalues and condition numbers of matrices, SIAM J. Numer. Anal., 20 (1983), pp. 812-814.
5. G.M. Engle and H. Schneider, The Hadamard-Fischer inequality for a class of matrices defined by eigenvalue monotonicity, Linear and Multilinear Algebra, 4 (1976), pp. 155-176.
6. R. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985.
7. C.R. Johnson, Optimization, matrix inequalities and matrix completions, in Operator Theory, Analytic Function, Matrices and Electrical Engineering, CBMS Reg. Conf. Ser. Math. 68, J.W. Melton, ed., AMS, Providence, RI, 1987.
8. C.R. Johnson and T. Markham, Compression and Hadamard power inequalities for M-matrices, Linear and Multilinear Algebra, 18 (1985), pp. 23-34.
9. C.R. Johnson and M. Newman, How bad is the Hadamard determinantal bound?, J. Res. Nat. Bureau Stand., 78 (1974), pp. 167-169.
10. A.G. Reznikov, A strengthened isoperimetric inequality for simplices, in Geometric Aspects of Functional Analysis (1989-90), Lecture Notes in Math. 1469, J. Lindenstrauss and V.D. Milmar, eds., Springer, New York, 1991, pp. 90-93.
11. A.G. Reznikov, Determinant inequalities with applications to isoperimetrical inequalities, in Geometric Aspects of Functional Analysis (Israel, 1992-94), Oper. Theory Adv. Appl. 77, Birkäuser, Basel, 1995, pp. 239-244.
12. J.S. Shiue, On a generalization of a theorem of Johnson and Newman, Soochow J. Math. Natur. Sci., 2 (1976), pp. 57-61.
13. D. Veljan, The sine theorem and inequalities for volume of simplices and determinants, Linear Algebra Appl., 219 (1995), pp. 79-91.
14. H. Wolkowitz and G. Styan, Bounds for eigenvalues using traces, Linear Algebra Appl., 29 (1980), pp. 471-506.
15. Zhang Xiaodong and Yang Shangjun, An improvement of Hadamard's inequality for totally nonnegative matrices, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 705-711.
16. Zhang Xiaodong and Yang Bhangjun, A note on Hadamard's inequality, Acta Math. Appl. Sinica, 20 (1997), pp. 269-274.