A direct proof for the matrix decomposition of chordal-structured positive semidefinite matrices

摘要: Agler, Helton, McCullough, and Rodman proved that a graph is chordal if only any positive semidefinite (PSD) symmetric matrix, whose nonzero entries are specified by given graph, can be decomposed as sum of PSD matrices corresponding to the maximal cliques. This decomposition recently exploited solve programming efficiently. Their proof based on characterization for matrix completion chordal-structured due Grone, Johnson, Sa, Wolkowicz. note gives direct simpler result Agler et al., which leads an alternative Grone al.