The Generalizations And Improvements Of Several Matrix Inequalities

In this paper,we establish a number of new matrix inequalities,extend and improve some relevant results.First,we prove some inverse Fischer inequalities involving the block Hadamard product and the Khatri-Rao product,the new inequalities could be regarded as complements of those of Choi,Liu et al.Then,we give a alternative generalization of Hartfiel's inequality to sector matrices,present a lower bound for det?++?,where,andare9)×9)positive definite matrices,obtain some lower bounds for det(??⁸)₄=1)₄)),where₄),4)=1,...,8)are9)×9)positive definite matrices,and extend the new inequalities to sector matrices.Next,we extend the Oppenheim-Schur inequalities to more than two positive semidefinite matrices,involving the Hadamard product and the block Hadamard product.Finally,we give an improvement of the Hadamard-Fischer inequality,present some complements of the results of 3×3 block matrices,extend some related inequalities to sector matrices.