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.
|Journal||Journal of Convex Analysis|
|Publication status||Published - 1 Jan 2005|