Determinant inequalities via information theory

Simple inequalities from information theory prove Hadamard's inequality and some of its gen- eralizations. It is also proven that the determinant ofa positive definite matrix is log-concave and that the ratio ofthe determinant ofthe matrix to the determinant of its principal minor g, I/Ig,- 1 is concave, establishing the concavity of minimum mean squared error in linear prediction. For Toeplitz matrices, the normalized determinant g, TM is shown to decrease with n.