International Journal of
Computer Engineering Research

  • Abbreviation: Int. J. Comput. Eng. Res.
  • Language: English
  • ISSN: 2141-6494
  • DOI: 10.5897/IJCER
  • Start Year: 2010
  • Published Articles: 29

Full Length Research Paper

New Holder-type inequalities for the Tracy-Singh and Khatri-Rao products of positive matrices

Zeyad AL-Zhour
Email: [email protected]

  •  Accepted: 02 April 2012
  •  Published: 31 May 2012



Recently, authors established a number of inequalities involving Khatri-Rao product of two positive matrices. Here, in this paper, the results are established in three ways. First, we find new Holder-type inequalities for Tracy-Singh and Khatri-Rao products of positive semi-definite matrices. Secondly, the results are extended to provide estimates of sums of the Khatri-Rao and Tracy-Singh products of any finite number of positive semi-definite matrices. Finally, the results lead to inequalities involving the Hadamard and Kronecker products, as a special case.


Key words: Tracy-Singh products, Khatri-Rao products, positive (semi) definite matrices, Holder inequalities