Abstract
Matrix polynomials with unitary or doubly stochastic coefficients form the subject matter of this manuscript. We prove that if \(P(\lambda )\) is a quadratic matrix polynomial whose coefficients are either unitary matrices or doubly stochastic matrices, then under certain conditions on these coefficients, the corresponding block companion matrix C is diagonalizable. Consequently, if \(Q(\lambda )\) is another quadratic matrix polynomial with corresponding block companion matrix D, then a Hoffman–Wielandt type inequality holds for the block companion matrices C and D.
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Acknowledgements
The authors are grateful to the referees for their valuable comments and suggestions. Pallavi Basavaraju and Shrinath Hadimani acknowledge the Council of Scientific and Industrial Research (CSIR) and the University Grants Commission (UGC), Government of India, for financial support through research fellowships.
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Communicated by Dragan S. Djordjevic.
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Basavaraju, P., Hadimani, S. & Jayaraman, S. Hoffman–Wielandt type inequality for block companion matrices of certain matrix polynomials. Adv. Oper. Theory 8, 65 (2023). https://doi.org/10.1007/s43036-023-00292-8
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DOI: https://doi.org/10.1007/s43036-023-00292-8
Keywords
- Matrix polynomials with unitary or doubly stochastic coefficients
- Eigenvalue bounds for matrix polynomials with doubly stochastic coefficients
- Diagonalizability of block companion matrix
- Hoffman–Wielandt type inequality