Comment on the paper

Manoj Joshi; K. N. Rajeshwari; K. Santaram; Sandeep Kanodia

doi:https://doi.org/10.14445/22315373/IJMTT-V53P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 1 | Year 2018 | Article Id. IJMTT-V53P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P502

Comment on the paper "Preserves of eigenvalue inclusion sets of matrix products"

Manoj Joshi, K. N. Rajeshwari, K. Santaram, Sandeep Kanodia

Citation :

Manoj Joshi, K. N. Rajeshwari, K. Santaram, Sandeep Kanodia, "Comment on the paper "Preserves of eigenvalue inclusion sets of matrix products"," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 1, pp. 9-12, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P502

Abstract

In [3], Theorem 2.1 deals with characterization of mappings 𝜙: 𝑀𝑛 → 𝑀𝑛 which satisfies 𝑂𝜀 𝜙 𝐴 𝜙 𝐵 = 𝑂𝜀 𝐴𝐵 , where 𝑂𝜀 𝐴 , 𝜀 ∈ 0,1 , denotes Ostrowski set of𝐴. In the proof of this theorem an assertion was made (assertion 2.6) whose proof contains an error. In this paper an example is provided to substantiate our claim and the error also has been rectified

Keywords

Eigen value, Inclusion sets, Preservers, Gershgorin Set, Ostrowski set.

References

[1] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
[2] R.S. Vargi, Gergorin and his circles, springs series in Computational Mathematics, vol. 36, Springer-Verlag, Berlin, 2004.
[3] V. Forstall, A. Herman, C. K. Li, N. S. Sze, V. Yannello. “Preservers of eigenvalue inclusion sets of matrix products” Linear Algebra Appl. 434 (2011), 285-293.