International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Review

Trace and determinant inequalities for Hadamard products

Mustafa Özel    
Division of Mathematics, Faculty of Engineering, Dokuz Eylul University, Tınaztepe Campus 35160, Buca, Ä°zmir, Turkey. 
Email: [email protected]

  •  Accepted: 15 December 2011
  •  Published: 02 January 2012

Abstract

In this paper, several inequalities involving positive integer powers of the Hadamard product of two matrices are presented. Firstly, a new upper bound for the product of their determinants and an inequality that relates the trace of the power of the Hadamard product of two matrices are given. Also, an alternative proof of the theorem established by Ulukok and Turkmen (2010) was given on the Frobenius norm of the power of the Hadamard product of two nonnegative matrices.

 

Key words: Hadamard product, trace inequalities, matrix norm.