The determinants of positive semidefinite matrices

In this thesis, determinant inequalities are studied. In the first part of our thesis, positive definite matrix, accretive-dissipative matrix, sector matrix notions have been introduced and determinant inequalities related to this matrices have been given. Also various important determinant inequalities like Hadamard determinant inequality, Fan determinant inequality, Fischer inequality have been mentioned. In the main part of thesis, some new determinant inequalities have been obtained.