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An extension of the generalised schur inequality

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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Abstract

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The well-known Schur inequality relates the sum of the squares of the absolute values of the eigenvalues of A to the elements of A. This was recently generalised to powers between one and two. Here we show that the inequality holds for powers between zero and two.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 341 - 343
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Ikramov, K.D., ‘A simple proof of the generalized Schur inequality’, Linear Algebra Appl. 199 (1994), 143–149.CrossRefGoogle Scholar
[2]Mirsky, L., An introduction to linear algebra (Oxford University Press, Oxford, 1955).Google Scholar
[3]Petri, N.V. and Ikramov, K.D., ‘Extremal properties of some matrix norms’, U.S.S.R. Comput. Math, and Math. Phys. 8 No. 4 (1968), 219–230.CrossRefGoogle Scholar