MINIMIZING THE CONDITION NUMBER OF A POSITIVE-DEFINITE MATRIX BY COMPLETION

We consider the problem of minimizing the spectral condition number of a positive definite matrix by completion: [GRAPHICS] where A is an n x n Hermitian positive definite matrix, B a p x n matrix and X is a fr ee p x p Hermitian matrix. We reduce this problem to an optimization p roblem for a convex function in one variable. Using the minimal soluti on of this problem we characterize the complete set of matrices that g ive the minimum condition number.