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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
Abstract

In [3], Theorem 2.1 deals with characterization of mappings ๐œ™: ๐‘€๐‘› โ†’ ๐‘€๐‘› which satisfies ๐‘‚๐œ€ ๐œ™ ๐ด ๐œ™ ๐ต = ๐‘‚๐œ€ ๐ด๐ต , where ๐‘‚๐œ€ ๐ด , ๐œ€ โˆˆ 0,1 , denotes Ostrowski set of๐ด. 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. โ€œPreservers of eigenvalue inclusion sets of matrix productsโ€ Linear Algebra Appl. 434 (2011), 285-293.

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

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