Abstract
We prove a generalization of Samuelson’s inequality for higher order central moments. Bounds for the eigenvalues are obtained when a given complex n × n matrix has real eigenvalues. Likewise, we discuss bounds for the roots of polynomial equations.
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Acknowledgements
The authors are grateful to Prof. Rajendra Bhatia for useful discussions and suggestions, and to ISI, Delhi for a visit in January 2013 when this work had begun. The support of the UGC-SAP is acknowledged.
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Communicating Editor: Parameswaran Sankaran
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SHARMA, R., SAINI, R. Generalization of Samuelson’s inequality and location of eigenvalues. Proc Math Sci 125, 103–111 (2015). https://doi.org/10.1007/s12044-015-0216-9
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DOI: https://doi.org/10.1007/s12044-015-0216-9