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Further inequalities involving the Khatri-Rao product |
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| Authors: | Zhongpeng Yang Götz Trenkler |
| Institution: | a Department of Mathematics, Putian University, Putian 351100, China b Faculty of Information Sciences and Engineering, University of Canberra, Canberra ACT 2601, Australia c Department of Statistics, University of Dortmund, D-44221 Dortmund, Germany |
| Abstract: | Styan G.P.H. Styan, Hadamard products and multivariate statistical analysis. Linear Algebra and Its Appl. 6 (1973) 217-240] established an inequality involving the Hadamard product using statistical reasoning in the context of multivariate analysis. In this paper, the inequality is extended to involve the Khatri-Rao product in the non-negative definite matrix case and in the non-singular Hermitian matrix case. The equality conditions for these extensions are given. Also established are counterpart inequalities in the positive definite matrix case. |
| Keywords: | Hadamard product Khatri-Rao product Tracy-Singh product Kronecker product Schur complement Matrix inequality |
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