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Liu, Xiao-Qin; Huang, Ting-Zhu; Fu, Ying-Ding

A note on improvement on bounds for nonmaximal eigenvalues of symmetric positive matrices. (English) Zbl 1151.15305

Linear Algebra Appl. 419, No. 2-3, 612-617 (2006).
Summary: We improve the lower and upper bounds obtained by X.-D. Zhang and R. Luo [Czech. Math. J. 52, No. 3, 537–544 (2002; Zbl 1014.15013)] for the nonmaximal eigenvalue \(\lambda _{n - 1}(A)\) of a symmetric positive matrix.

Cited in 2 Documents

MSC:

15A42 Inequalities involving eigenvalues and eigenvectors
15B48 Positive matrices and their generalizations; cones of matrices

Keywords:

nonmaximal eigenvalue; symmetric positive matrix

Citations:

Zbl 1014.15013
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Full Text: DOI

References:

[1] Zhang, X.; Luo, R., Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices, Czechoslovak Math. J., 52, 127, 537-544 (2002) · Zbl 1014.15013
[2] Walker, S. G., Improving bounds for nonmaximal eigenvalues of positive matrices, Linear Algebra Appl., 397, 133-139 (2005) · Zbl 1074.15027
[3] Nabben, R., Improved upper bounds for the real part of nonmaximal eigenvalues of nonnegative matrices, SIAM J. Matrix Anal. Appl., 22, 574-579 (2000) · Zbl 1039.15010
[4] Berman, A.; Zhang, X., Lower bounds for the eigenvalues of Laplacian matrices, Linear Algebra Appl., 316, 13-20 (2000) · Zbl 0958.15014
[5] Friedland, S.; Nabben, R., On the second real eigenvalue of nonnegative and Z-matrix, Linear Algebra Appl., 255, 301-313 (1997) · Zbl 0874.15011
[6] Friedland, S.; Nabben, R., On Cheeger-type inequalities for weighted graphs, J. Graph Theory, 1, 41, 1-17 (2002) · Zbl 1005.05028
[7] Walker, S. G., On recent Cheeger type bounds for nonmaximal eigenvalues applied to positive matrices, SIAM J. Matrix Anal. Appl., 25, 574-581 (2003) · Zbl 1057.15024
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