Generalization of Oppenheim Type Inequality for quasi-generalized complex positive definite matrices
Yang Zhong-peng · Journal of Natural Science of Heilongjiang University · 2006
The strengthened form of the classical Oppenheim Type Inequality for estimating the lower bound of the determinant on the Hadamard product of Hermitian positive definite matrices is improved. Furthermore, a new estimation of the lower bound of the determinant module on the Hadamard product of a Hermitian positive definite matrix and a quasi-generalized complex positive definite matrix is obtained by using the improvement and the properties of quasi-generalized complex positive definite matrices. These results not only generalize and improve the corresponding results on quasi-generalized complex positive definite matrices in the recent relevant papers, but also summarize the classical Oppenheim Type Inequality for estimating the lower bound of the determinant on the Hadamard product of real positive definite matrices and metapositive definite matrices.