Many Results Of Generalized Complex Positive Definite Matrices

In recent years, the research for matrices produce great improvement. The discussion of positive definite matrix plays a very important role in matrix analysis and computation. Especially, the generalized positive definite property of complex (real) matrix and its connected problems produce many new production.In this paper, we discuss some classification of the generalized complex positive definite matrix. First, the concept of generalized complex positive definite matrix is given, and its basic properties are discussed. Thus some new results are obtained. Second, we prove several special results of the generalized complex positive definite matrix. Therefore, we make improvement on the research of generalized complex positive definite matrix. Meanwhile, we give some corresponding results of connected problems of the generalized complex positive definite matrix.