Geodesic
New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 63-68

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.1007/s10587-014-0083-z
Classification : 15A18, 15A42, 15B48
Keywords: Fan product; minimum eigenvalue; $M$-matrix 
Cheng, Guanghui. New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 1, pp. 63-68. doi: 10.1007/s10587-014-0083-z
@article{10_1007_s10587_014_0083_z,
     author = {Cheng, Guanghui},
     title = {New bounds for the minimum eigenvalue of the {Fan} product of two $M$-matrices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {63--68},
     year = {2014},
     volume = {64},
     number = {1},
     doi = {10.1007/s10587-014-0083-z},
     mrnumber = {3247444},
     zbl = {06391476},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0083-z/}
}
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
SP  - 63
EP  - 68
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0083-z/
DO  - 10.1007/s10587-014-0083-z
LA  - en
ID  - 10_1007_s10587_014_0083_z
ER  - 
%0 Journal Article
%A Cheng, Guanghui
%T New bounds for the minimum eigenvalue of the Fan product of two $M$-matrices
%J Czechoslovak Mathematical Journal
%D 2014
%P 63-68
%V 64
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0083-z/
%R 10.1007/s10587-014-0083-z
%G en
%F 10_1007_s10587_014_0083_z

[1] Berman, A., Plemmons, R. J.: Nonnegative Matrices in the Mathematical Sciences. Classics in Applied Mathematics 9 SIAM, Philadelphia (1994). | MR | Zbl

[2] Fang, M. Z.: Bounds on eigenvalues of the Hadamard product and the Fan product of matrices. Linear Alegebra. Appl. 425 (2007), 7-15. | DOI | MR | Zbl

[3] Horn, R. A., Johnson, C. R.: Topics in Matrix Analysis. Cambridge University Press Cambridge (1991). | MR | Zbl

[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. | MR | Zbl

Cité par Sources :