TOEPLITZ AND POSITIVE SEMIDEFINITE COMPLETION PROBLEM FOR CYCLE GRAPH

We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefinite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those given in 1] for a simple cycle. We also derive some results for a partial Toeplitz PSD matrix specifying the Cnk pattern to have PSD completion and Toeplitz PSD completion.