Previous |  Up |  Next


matrix inequality; Khatri-Rao product; Tracy-Singh product; Hadamard product; Kronecker product; Schur complement
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.
[1] Amemiya: Advanced econometrics. University Press, Cambridge, USA, 1985.
[2] Bo-Ying Wang, Fuzhen Zhang: Schur complements and matrix inequalities of Hadamard products. Linear and Multilinear Algebra 43 (1997), 315–326. MR 1613081
[3] Horn R. A., Johnson C. R.: Matrix analysis. Cambridge University Press, New York, 1985. MR 0832183 | Zbl 0576.15001
[4] Marcus M., Khan N. A.: A note on the Hadamard product. Canad. Math. Bull. 2 (1959), 81–83. MR 0105424 | Zbl 0092.01602
[5] Mond B., Pecaric J. E.: Inequalities for the Hadamard product of matrix. SIAM J. Matrix Anal. Appl., 19 (1) (1998), 66–70. MR 1610004
[6] Shuangzhe Liu: Matrix results on the Khatri-Rao and Tracy-Singh products. Linear Algebra Appl. 289 (1999), 266–277. MR 1670989
[7] Shuangzhe Liu: Inequalities involving Hadamard products of positive semidefinite matrices. J. Math. Anal. Appl. 243 (2000), 458–463. MR 1741535
[8] Zhan Xingzhi: Inequalities involving Hadamard products and unitarily invariant norms. Adv. Math. 27 (5) (1998), 416–422. MR 1711666 | Zbl 1054.15503
Partner of
EuDML logo