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Indefinite numerical range of 3 × 3 matrices

N. Bebiano, J. da Providência, R. Teixeira (2009)

Czechoslovak Mathematical Journal

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.

Inertial law of quadratic forms on modules over plural algebra

Marek Jukl (1995)

Mathematica Bohemica

Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over ( real plural algebra) introduced in [1].

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