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Determinant and eigenvalue inequalities involving nonnegative matrices

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Abstract

We discuss some bounds for the determinant of a matrix when all its eigenvalues are positive as in case of totally positive matrices. We further show how positive unital linear maps can be used to obtain some bounds for the eigenvalues of Hermitian and nonnegative matrices.

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Acknowledgements

The authors are grateful to Prof. Rajendra Bhatia for useful discussions and suggestions and also thank Ashoka University for a visit in Jan–Feb 2023.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, H.P. University, Shimla, 5, India

    Rajesh Sharma, Manish Pal & Anjana Sharma

Authors
  1. Rajesh Sharma
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  2. Manish Pal
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  3. Anjana Sharma
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Correspondence to Manish Pal.

Additional information

Communicated by Kenneth Berenhaut.

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Sharma, R., Pal, M. & Sharma, A. Determinant and eigenvalue inequalities involving nonnegative matrices. Adv. Oper. Theory 8, 55 (2023). https://doi.org/10.1007/s43036-023-00283-9

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