Moment-entropy inequalities for a random vector

Erwin Lutwak, Deane Yang, Gaoyong Zhang

Research output: Contribution to journalArticlepeer-review


The pth moment matrix is defined for a real random vector, generalizing the classical covariance matrix. Sharp inequalities relating the pth moment and Renyi entropy are established, generalizing the classical inequality relating the second moment and the Shannon entropy. The extremal distributions for these inequalities are completely characterized.

Original languageEnglish (US)
Pages (from-to)1603-1607
Number of pages5
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2007


  • Covariance
  • Covariance matrix
  • Entropy
  • Information measure
  • Information theory
  • Moment
  • Moment matrix
  • Random vector
  • Renyi entropy

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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