On Brickman's Theorem

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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 whose component functions are quadratic forms. We also discuss some consequences of this theorem regarding the range of that mapping. © Heldermann Verlag Quadratic forms, convexity.
Original languageEnglish
Pages (from-to)139-143
JournalJournal of Convex Analysis
Volume12
Issue number1
Publication statusPublished - 1 Jan 2005

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