Löwner partial ordering and space preordering of Hermitian non-negative definite matrices Original Research Article

If a matrix A is below a matrix B with respect to the Löwner partial ordering within the set of Hermitian non-negative definite matrices, then the columns of A are linear combinations of the columns of B. In this note, the class of all such combinations providing a complete characterization of the Löwner partial ordering is presented. In addition, new results on partial ordering of squares of Hermitian non-negative definite matrices are given.