Optimal l1 factorizations of positive semidefinite matrices


Among infinitely many factorizations A=VV* of a psd matrix A, we seek the factor V that has the smallest (1,2) norm. In this talk we review the origin of this problem as well as existing results regarding the optimal value. We discuss also the conjecture that the squared (1,2) norm of V is equivalent to the (1,1) norm of A.