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Indefinite numerical range of 3 × 3 matrices

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Abstract

The point equation of the associated curve of the indefinite numerical range is derived, following Fiedler’s approach for definite inner product spaces. The classification of the associated curve is presented in the 3 × 3 indefinite case, using Newton’s classification of cubic curves. Illustrative examples of all the different possibilities are given. The results obtained extend to Krein spaces results of Kippenhahn on the classical numerical range.

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Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, Coimbra, Portugal

    N. Bebiano

  2. Department of Physics, University of Coimbra, Coimbra, Portugal

    J. da Providência

  3. CMUC and Department of Mathematics, University of Azores, Azores, Portugal

    R. Teixeira

Authors
  1. N. Bebiano
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  2. J. da Providência
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  3. R. Teixeira
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Corresponding author

Correspondence to N. Bebiano.

Additional information

The work of this author was partially supported by the Portuguese foundation FCT, in the scope of program POCI 2010.

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Bebiano, N., da Providência, J. & Teixeira, R. Indefinite numerical range of 3 × 3 matrices. Czech Math J 59, 221–239 (2009). https://doi.org/10.1007/s10587-009-0016-4

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  • DOI: https://doi.org/10.1007/s10587-009-0016-4

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