Resumen de Every convex free basic semi-algebraic set has an LMI representation

J. William Helton, Scott McCullough

• The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex free basic open semi-algebraic set. The main theorem of this paper is a converse, each such set arises from some LMI. The result has implications for semi-definite programming and systems engineering as well as for free semi-algebraic geometry.