Determinant Inequalities via Information Theory

Abstract

Simple inequalities from information theory prove Hadamard’s inequality and some of its generalizations. It is also proven that the determinant of a positive definite matrix is log-concave and that the ratio of the determinant of the 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. Key words, inequalities, entropy, Hadamard, determinants AMS(MOS) subject classification. 94A 15

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@inproceedings{Thomas2007DeterminantIV, title={Determinant Inequalities via Information Theory}, author={Aleyamma Thomas}, year={2007} }