Geodesic
Indefinite numerical range of $3\times 3$ matrices
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 221-239 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $3\times 3$ 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.
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 $3\times 3$ 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.
Classification : 15A60, 15A63, 46C20
Keywords: indefinite numerical range; indefinite inner product space; plane algebraic curve 
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     author = {Bebiano, N. and Provid\^encia, J. da and Teixeira, R.},
     title = {Indefinite numerical range of $3\times 3$ matrices},
     journal = {Czechoslovak Mathematical Journal},
     pages = {221--239},
     year = {2009},
     volume = {59},
     number = {1},
     mrnumber = {2486627},
     zbl = {1224.15043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a15/}
}
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Bebiano, N.; Providência, J. da; Teixeira, R. Indefinite numerical range of $3\times 3$ matrices. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 1, pp. 221-239. http://geodesic.mathdoc.fr/item/CMJ_2009_59_1_a15/