Geodesic
Matrix inequalities involving the Khatri-Rao product
Archivum mathematicum, Tome 38 (2002) no. 4, pp. 265-272 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We extend three inequalities involving the Hadamard product in three ways. First, the results are extended to any partitioned blocks Hermitian matrices. Second, the Hadamard product is replaced by the Khatri-Rao product. Third, the necessary and sufficient conditions under which equalities occur are presented. Thereby, we generalize two inequalities involving the Khatri–Rao product.
We extend three inequalities involving the Hadamard product in three ways. First, the results are extended to any partitioned blocks Hermitian matrices. Second, the Hadamard product is replaced by the Khatri-Rao product. Third, the necessary and sufficient conditions under which equalities occur are presented. Thereby, we generalize two inequalities involving the Khatri–Rao product.
Classification : 15A45, 15A69
Keywords: matrix inequality; Khatri-Rao product; Tracy-Singh product; Hadamard product; Kronecker product; Schur complement 
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     author = {Zhang, Xian and Yang, Zhong-Peng and Cao, Chong-Guang},
     title = {Matrix inequalities involving the {Khatri-Rao} product},
     journal = {Archivum mathematicum},
     pages = {265--272},
     year = {2002},
     volume = {38},
     number = {4},
     mrnumber = {1942656},
     zbl = {1090.15015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a2/}
}
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Zhang, Xian; Yang, Zhong-Peng; Cao, Chong-Guang. Matrix inequalities involving the Khatri-Rao product. Archivum mathematicum, Tome 38 (2002) no. 4, pp. 265-272. http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a2/