| Title:
|
New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices (English) |
| Author:
|
Cheng, Guanghui |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
63-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we mainly use the properties of the minimum eigenvalue of the Fan product of $M$-matrices and Cauchy-Schwarz inequality, and propose some new bounds for the minimum eigenvalue of the Fan product of two $M$-matrices. These results involve the maximum absolute value of off-diagonal entries of each row. Hence, the lower bounds for the minimum eigenvalue are easily calculated in the practical examples. In theory, a comparison is given in this paper. Finally, to illustrate our results, a simple example is also considered. (English) |
| Keyword:
|
Fan product |
| Keyword:
|
minimum eigenvalue |
| Keyword:
|
$M$-matrix |
| MSC:
|
15A18 |
| MSC:
|
15A42 |
| MSC:
|
15B48 |
| idZBL:
|
Zbl 06391476 |
| idMR:
|
MR3247444 |
| DOI:
|
10.1007/s10587-014-0083-z |
| . |
| Date available:
|
2014-09-29T09:33:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143949 |
| . |
| Reference:
|
[1] Berman, A., Plemmons, R. J.: Nonnegative Matrices in the Mathematical Sciences.Classics in Applied Mathematics 9 SIAM, Philadelphia (1994). Zbl 0815.15016, MR 1298430 |
| Reference:
|
[2] Fang, M. Z.: Bounds on eigenvalues of the Hadamard product and the Fan product of matrices.Linear Alegebra. Appl. 425 (2007), 7-15. Zbl 1128.15011, MR 2334489, 10.1016/j.laa.2007.03.024 |
| Reference:
|
[3] Horn, R. A., Johnson, C. R.: Topics in Matrix Analysis.Cambridge University Press Cambridge (1991). Zbl 0729.15001, MR 1091716 |
| Reference:
|
[4] Liu, Q. B., Chen, G. L.: On two inequalities for the Hadamard product and the Fan product of matrices.Linear Algebra Appl. 431 (2009), 974-984. Zbl 1183.15017, MR 2535567 |
| . |
