Matrix inequalities involving the Khatri-Rao product
Xian Zhang; Zhong Peng Yang; Chong-Guang Cao
Archivum Mathematicum (2002)
- Volume: 038, Issue: 4, page 265-272
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topZhang, Xian, Yang, Zhong Peng, and Cao, Chong-Guang. "Matrix inequalities involving the Khatri-Rao product." Archivum Mathematicum 038.4 (2002): 265-272. <http://eudml.org/doc/248936>.
@article{Zhang2002,
abstract = {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.},
author = {Zhang, Xian, Yang, Zhong Peng, Cao, Chong-Guang},
journal = {Archivum Mathematicum},
keywords = {matrix inequality; Khatri-Rao product; Tracy-Singh product; Hadamard product; Kronecker product; Schur complement; Khatri-Rao product; Tracy-Singh product; Hadamard product; Kronecker product; Schur complement},
language = {eng},
number = {4},
pages = {265-272},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Matrix inequalities involving the Khatri-Rao product},
url = {http://eudml.org/doc/248936},
volume = {038},
year = {2002},
}
TY - JOUR
AU - Zhang, Xian
AU - Yang, Zhong Peng
AU - Cao, Chong-Guang
TI - Matrix inequalities involving the Khatri-Rao product
JO - Archivum Mathematicum
PY - 2002
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 038
IS - 4
SP - 265
EP - 272
AB - 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.
LA - eng
KW - matrix inequality; Khatri-Rao product; Tracy-Singh product; Hadamard product; Kronecker product; Schur complement; Khatri-Rao product; Tracy-Singh product; Hadamard product; Kronecker product; Schur complement
UR - http://eudml.org/doc/248936
ER -
References
top- Amemiya, Advanced econometrics, University Press, Cambridge, USA, 1985. (1985)
- Bo-Ying Wang, Fuzhen Zhang, Schur complements and matrix inequalities of Hadamard products, Linear and Multilinear Algebra 43 (1997), 315–326. (1997) MR1613081
- Horn R. A., Johnson C. R., Matrix analysis, Cambridge University Press, New York, 1985. (1985) Zbl0576.15001MR0832183
- Marcus M., Khan N. A., A note on the Hadamard product, Canad. Math. Bull. 2 (1959), 81–83. (1959) Zbl0092.01602MR0105424
- Mond B., Pecaric J. E., Inequalities for the Hadamard product of matrix, SIAM J. Matrix Anal. Appl., 19 (1) (1998), 66–70. (1998) MR1610004
- Shuangzhe Liu, Matrix results on the Khatri-Rao and Tracy-Singh products, Linear Algebra Appl. 289 (1999), 266–277. (1999) MR1670989
- Shuangzhe Liu, Inequalities involving Hadamard products of positive semidefinite matrices, J. Math. Anal. Appl. 243 (2000), 458–463. MR1741535
- Zhan Xingzhi, Inequalities involving Hadamard products and unitarily invariant norms, Adv. Math. 27 (5) (1998), 416–422. (1998) Zbl1054.15503MR1711666
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.