We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (PSD) completion. Since the graph of the Cnk pattern is composed by some simple cycles, our results extend those...We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (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.展开更多
基金Research supported in part by National Natural Science Foundation of China No. 10271099. Research supported in part by RGC Grant Nos. 7132/OOP and 7130/02PHKU CRCG Grant Nos 10203501, and 10204437.
文摘We present a sufficient and necessary condition for a so-called Cnk pattern to have positive semidefnite (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.
