Abstract
The numerical range of a linear pencil (A, B) of matrices of size n, of which either A or B is Hermitian , may be characterized in terms of a certain algebraic curve of class n, called the boundary generating curve. This curve is explicitly given by the characteristic polynomial of the pencil . For \(n=2\) and \(n=3\), each possible type of boundary generating curve can be completely described. For \(n=3\), the curve type is given by Newton’s classification of cubic curves . Illustrative examples of the different possibilities are given.
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Acknowledgements
This work was partially supported by the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.
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Bebiano, N., da Providência, J., Esmaeili, F. (2017). The Characteristic Polynomial of Linear Pencils of Small Size and the Numerical Range. In: Bebiano, N. (eds) Applied and Computational Matrix Analysis. MAT-TRIAD 2015. Springer Proceedings in Mathematics & Statistics, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-49984-0_13
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DOI: https://doi.org/10.1007/978-3-319-49984-0_13
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