Norm of nonnegative and positive matrices
Keywords:Nonnegative Matrix, Positive Matrix, Spectral Radius, Perron Roots of Nonnegative Matrix.
The spectral radius r(A) of matrix A is the maximum modulus of the Eigen values. In this paper, the studies about the lower and upper bounds for the spectral radius and the lower bounds for the minimum eigen value of appositive and nonnegative matrices are investigate.
The matrix norm, the spectral radius norm,and the column (row) sums of nonnegative and positive matrices are widely used to establish some inequalities for matrices. Then several existing results are improved for these inequalities for nonnegative and positive matrix. Furthermore, the lower and upper bounds of the Perron roots for nonnegative matrices are examined, and some upper bounds are computed.
 Barraa, M. and Boumazgour, M. (2001). Inner derivations and norm equality,Proc. Amer. Math. Soc. 130:471-476.https://doi.org/10.1090/S0002-9939-01-06053-1.
 Bhatia, R. (1997). Matrix Analysis, Springer-Verlag, New York.https://doi.org/10.1007/978-1-4612-0653-8.
 Cheng, G-H., Cheng, X-Y., Huang, T-Z., and Tam, T-Y. (2005). Some Bounds for the spectralradius of the Hadamrad product of matrices, Applied Math. E-Notes. 5: 202-209
 Fujii, M. and Kubo, F. (1993). Buzanoâ€™s inequality and bounds for roots of algebraic equations, proc. Amer. math. soc. 117:359-361.
 Halmos, P.R. (1982). A Hillbert Space Problem Book, 2nd ed., Springer-Verlag, New York. https://doi.org/10.1007/978-1-4684-9330-6.
 Horn, R. A. and Johnson, C. R. (1985). Matrix Analysis, Cambridge University Press, Cambridge.https://doi.org/10.1017/CBO9780511810817.
 Horn, R. A. and Johnson, C.R. (1991). Topics in Matrix Analysis, Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511840371.
 Hou, I.C. and Du, H. K. (1995). Norm inequalities of positive operator matrices, Integral Equations Operator Theory 22:281-294.https://doi.org/10.1007/BF01378777.
 Kittaneh, F. (2002). Norm inequalities for sums of positive operator, J. Operator Theory 48:95-103.
 Kittaneh, F.2003. A numerical radius inequality and an estimate for the numerical radius of the Forbenius companion matrix, StudiaMath.158:11-17. https://doi.org/10.4064/sm158-1-2.
 Kittaneh, F. (2005). Spectral radius inequalities for Hilbert Space operato, Porc. Amer. math. Soc.143:385-390
 Kittaneh, F. (2005). Numerical radius inequalities for Hilbert Space operator,Studia Math., 168:73-80.https://doi.org/10.4064/sm168-1-5.
 Omladic, M., Radjavi, H., Rosenthal, P., and Sourour, A. (2001). Inequalities for the products of spectural radii, Proc. Amer. Math. Soc. 129:2239-2243.https://doi.org/10.1090/S0002-9939-01-05500-9.
 Tasci, D. and Celik, H. A. On the upper bounds of the Perron roots of nonnegative matrices, Selcuk University, Konya, Turkey. Math., to appear.
 Zhang, F. (1999). Matrix Theory, Springer- Verlag, New York.https://doi.org/10.1007/978-1-4757-5797-2.
View Full Article:
Authors who publish with this journal agree to the following terms:
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under aÂ Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (SeeÂ The Effect of Open Access).