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Research articles

ScienceAsia 35 (2009): 106-110 |doi: 10.2306/scienceasia1513-1874.2009.35.106


Inequalities for Kronecker products and Hadamard products of positive definite matrices


Pattrawut Chansangiam*, Patcharin Hemchote, Praiboon Pantaragphong

 
ABSTRACT:     The purpose of this paper is to develop inequalities for Kronecker products and Hadamard products of positive definite matrices. A number of inequalities involving powers, Kronecker powers, and Hadamard powers of linear combination of matrices are presented. In particular, Hölder inequalities and arithmetic mean-geometric mean inequalities for Kronecker products and Hadamard products are obtained as special cases.

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Department of Mathematics and Computer Science, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand

* Corresponding author, E-mail: kcpattra@kmitl.ac.th

Received 9 Oct 2008, Accepted 15 Jan 2009