New bounds for the minimum eigenvalue of the Fan product of two -matrices
Czechoslovak Mathematical Journal (2014)
- Volume: 64, Issue: 1, page 63-68
- ISSN: 0011-4642
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topCheng, Guanghui. "New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices." Czechoslovak Mathematical Journal 64.1 (2014): 63-68. <http://eudml.org/doc/262026>.
@article{Cheng2014,
abstract = {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.},
author = {Cheng, Guanghui},
journal = {Czechoslovak Mathematical Journal},
keywords = {Fan product; minimum eigenvalue; $M$-matrix; Fan product; minimum eigenvalue; -matrix; Cauchy-Schwarz inequality; lower bounds},
language = {eng},
number = {1},
pages = {63-68},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices},
url = {http://eudml.org/doc/262026},
volume = {64},
year = {2014},
}
TY - JOUR
AU - Cheng, Guanghui
TI - New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 1
SP - 63
EP - 68
AB - 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.
LA - eng
KW - Fan product; minimum eigenvalue; $M$-matrix; Fan product; minimum eigenvalue; -matrix; Cauchy-Schwarz inequality; lower bounds
UR - http://eudml.org/doc/262026
ER -
References
top- Berman, A., Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics 9 SIAM, Philadelphia (1994). (1994) Zbl0815.15016MR1298430
- Fang, M. Z., 10.1016/j.laa.2007.03.024, Linear Alegebra. Appl. 425 (2007), 7-15. (2007) Zbl1128.15011MR2334489DOI10.1016/j.laa.2007.03.024
- Horn, R. A., Johnson, C. R., Topics in Matrix Analysis, Cambridge University Press Cambridge (1991). (1991) Zbl0729.15001MR1091716
- 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. (2009) Zbl1183.15017MR2535567
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