Abstract
The Schur theorem provides the global bounds for spectrum of the Hadamard product of two positive semi-definite matrices. In this paper, we obtain lower and upper estimations for each eigenvalue of the Hadamard product of two Hermitian matrices.
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References
R. A. Horn. 1990. The Hadamard Product. In Proceedings of Symposia in Applied Mathematics, ed. Charles R. Johnson, Vol: 40, pp. 87–169. American Mathematical Society, RI, x+260.
Horn, R.A., and C.R. Johnson. 1991. Topics in matrix analysis. Cambridge: Cambridge Univ. Press.
Horn, R.A., and C.R. Johnson. 2013. Matrix analysis, 2nd ed. Cambridge: Cambridge Univ. Press.
Lancaster, P. 1969. Theory of Matrices. New York: Academic.
Wang, S.G., and S.C. Chow. 1994. Advanced linear model: Theory and applications. New York: Marcel Dekker.
B. V. Rajarama Bhat, Arup Chattopadhyay and G. Sankara Raju Kosuru, On submajorization and eigenvalue inequalities, to appear in Linear and Multilinear Algebra. http://www.tandfonline.com/doi/pdf/10.1080/03081087.2014.1000817.
Eric Iksoon Im. 1997. Narrower eignebounds for Hadarmard Product. Linear Algebra and its Applications 264: 141–144.
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The author would like to thank the reviewer and Dr. D. Venku Naidu for useful comments and suggestions.
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The work is support by ISIRD project (Ref. No. IITRPR/Acad./526) from Indian Institute of Technology Ropar.
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Kosuru, G.S.R. Specific eigenbounds for Hadamard product of Hermitian matrices. J Anal 28, 3–8 (2020). https://doi.org/10.1007/s41478-017-0029-6
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DOI: https://doi.org/10.1007/s41478-017-0029-6