Further subadditive matrix inequalities

Matrix inequalities that extend certain scalar ones have been in the center of numerous researchers' attention. In this article, we explore the celebrated subadditive inequality for matrices via concave functions and present a reversed version of this result. Our approach will be tackling concave functions properties and some delicate manipulations of matrices and inner product properties. Once this has been done, concavity approach is implemented to show many sub and super additive inequalities for the determinant. This approach is a new direction in this type of inequalities. In the end, many determinant inequalities are presented for accretive-dissipative matrices.