| Title:
|
The equality cases for the inequalities of Oppenheim and Schur for positive semi-definite matrices (English) |
| Author:
|
Zhang, Xiao-Dong |
| Author:
|
Ding, Chang-Xing |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
197-206 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, necessary and sufficient conditions for equality in the inequalities of Oppenheim and Schur for positive semidefinite matrices are investigated. (English) |
| Keyword:
|
Oppenheim's inequality |
| Keyword:
|
Schur's inequality |
| Keyword:
|
positive semidefinite matrix |
| Keyword:
|
Hadamard product |
| MSC:
|
15A45 |
| MSC:
|
15A57 |
| idZBL:
|
Zbl 1224.15042 |
| idMR:
|
MR2486625 |
| . |
| Date available:
|
2010-07-20T15:00:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140473 |
| . |
| Reference:
|
[1] Bapat, R. B., Ragharan, T. E. S.: Nonnegative Matrices and Applications.Cambridge University Press (1997). MR 1449393 |
| Reference:
|
[2] Bapat, R. B., Sunder, V. S.: On majorization and Schur products.Linear Algebra and its Applications 72 (1985), 107-117. Zbl 0577.15016, MR 0815257 |
| Reference:
|
[3] Fallat, S. M., Johnson, C. R.: Determinantal inequalities: ancient history and recent advances, Algebra and its Applications (Athens, OH, 1999), 199-212.Contemporary Math. 259, Amer. Math. Soc., Providence, RI (2000). MR 1778502 |
| Reference:
|
[4] Horn, R. A., Johnson, C. R.: Topics in Matrix Analysis.Cambridge University Press (1991). Zbl 0729.15001, MR 1091716 |
| Reference:
|
[5] Marshall, A. W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications.Academic Press (1979). Zbl 0437.26007, MR 0552278 |
| Reference:
|
[6] Mirsky, L.: An introduction to linear algebra.Oxford University, Oxford (1955). Zbl 0066.26305, MR 0074364 |
| Reference:
|
[7] Oppenheim, A.: Inequalities connected with definite Hermitian forms.J. London Math. Soc. 5 (1930), 114-119. MR 1574213, 10.1112/jlms/s1-5.2.114 |
| . |
