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Inequalities with weights for powers of generalised inverses

Published online by Cambridge University Press:  17 April 2009

B. Mond  and
J.E. Pečarić
B. Mond
Affiliation:
Department of Mathematics, La Trobe University, Bundoora Vic 3083, Australia
J.E. Pečarić
Affiliation:
Faculty of Textile Technology, University of Zagreb, Zagreb Croatia and Department of Mathematics La Trobe University Bundoora Vic 3083, Australia
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Recently the authors extended to positive semi-definite matrices converses of matrix inequalities corresponding to ratios and differences of means and of Hölder's inequality. Here, further generalisations are given to the case of several vectors with appropriate weights.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 7 - 12
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Fan, K., ‘Some matrix inequalities’, Abh. Math. Sem. Univ. Hamburg 29 314 (1966), 185–196.CrossRefGoogle Scholar
[2]Hearon, J.Z., ‘A generalized matrix version of Rennie's inequality’, J. Res. Nat. Bur. Standard (Math, and Math. Phys.) 71B (1967), 61–64.CrossRefGoogle Scholar
[3]Mond, B. and Pečarić, J.E., ‘Inequalities involving powers of generalized inverses’, Linear Algebra Appl. (to appear).Google Scholar