Probabilistic factorization of a quadratic matrix polynomial

Source abstract

A purely algebraic result . We begin by stating the following theorem. Theorem. Let E be a finite set, and let denote the set of real E × E matrices with non-negative off-diagonal elements and with non-positive row sums. Let A be a symmetric element of , and let V be a diagonal real E × E matrix. Then there exists a unique pair (H + , H − ) of elements of such that I denoting the identity E × E matrix, and the superscript T signifying transpose. It is an immediate consequence that