Sums of Squares: A Real Projective Story

Abstract

How do we find the minimum of the function 2( 2 − ) on the unit sphere? An algebraic way to see that the minimum equals −1 involves the decompositionThe unit sphere in ℝ 3 is the zero-locus of the polynomial 1 − 2 − 2 − 2 . This decomposition establishes that the