• DOI:10.1137/0609033
Corpus ID: 5491763

Determinant inequalities via information theory

@article{Cover1988DeterminantIV,
  title={Determinant inequalities via information theory},
  author={T. Cover and J. Thomas},
  journal={SIAM Journal on Matrix Analysis and Applications},
  year={1988},
  volume={9},
  pages={384-392}
}

T. Cover, J. Thomas

Published 1988

Mathematics

SIAM Journal on Matrix Analysis and Applications

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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.