| Title:
|
Matrix inequalities involving the Khatri-Rao product (English) |
| Author:
|
Zhang, Xian |
| Author:
|
Yang, Zhong-Peng |
| Author:
|
Cao, Chong-Guang |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
265-272 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
matrix inequality |
| Keyword:
|
Khatri-Rao product |
| Keyword:
|
Tracy-Singh product |
| Keyword:
|
Hadamard product |
| Keyword:
|
Kronecker product |
| Keyword:
|
Schur complement |
| MSC:
|
15A45 |
| MSC:
|
15A69 |
| idZBL:
|
Zbl 1090.15015 |
| idMR:
|
MR1942656 |
| . |
| Date available:
|
2008-06-06T22:30:55Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107840 |
| . |
| Reference:
|
[1] Amemiya: Advanced econometrics.University Press, Cambridge, USA, 1985. |
| Reference:
|
[2] Bo-Ying Wang, Fuzhen Zhang: Schur complements and matrix inequalities of Hadamard products.Linear and Multilinear Algebra 43 (1997), 315–326. MR 1613081 |
| Reference:
|
[3] Horn R. A., Johnson C. R.: Matrix analysis.Cambridge University Press, New York, 1985. Zbl 0576.15001, MR 0832183 |
| Reference:
|
[4] Marcus M., Khan N. A.: A note on the Hadamard product.Canad. Math. Bull. 2 (1959), 81–83. Zbl 0092.01602, MR 0105424 |
| Reference:
|
[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 |
| Reference:
|
[6] Shuangzhe Liu: Matrix results on the Khatri-Rao and Tracy-Singh products.Linear Algebra Appl. 289 (1999), 266–277. MR 1670989 |
| Reference:
|
[7] Shuangzhe Liu: Inequalities involving Hadamard products of positive semidefinite matrices.J. Math. Anal. Appl. 243 (2000), 458–463. MR 1741535 |
| Reference:
|
[8] Zhan Xingzhi: Inequalities involving Hadamard products and unitarily invariant norms.Adv. Math. 27 (5) (1998), 416–422. Zbl 1054.15503, MR 1711666 |
| . |
