Abstract

We give an elementary proof of a theorem of Brickman, which establishes the convexity of the image of the unit sphere of a space with dimension at least three under a vector mapping into R2\mathbb{R}^2 whose component functions are quadratic forms. We also discuss some consequences of this theorem regarding the range of that mapping.

Author information

Contact details are reproduced from the original publication and may be historical.

Juan Enrique Martínez-Legaz

CODE and Departament d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

JuanEnrique.Martinez@uab.es

Keywords

  • Quadratic forms
  • convexity

Mathematics Subject Classification

15A63, 52A10

References

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Suggested citation

J. E. Martínez-Legaz. “On Brickman's Theorem.” Journal of Convex Analysis 12 (2005), No. 1, 139–143. https://doi.org/10.68381/jca12009

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.