On a Decomposition of Conditionally Positive Semidefinite Matrices

摘要

The necessary and sufficient conditions on a given matrix A under which every A conditionally positive semidefinite matrix Q admits a decomposition of the form Q=A'CA + S (with C strictly copositive and S positive semidefinite) are established. A theorem is proved which states that it is necessary and sufficient that A should possess the closure property together with either the column rank or Slater's property.