In this paper we derive explicit formulas for computing the roots of a quadratic polynomial with coefficients in a generalized quaternion algebra over any field F with characteristic not 2. We also give some example of applications for the derived formulas, solving equations in the algebra of Hamilton’s quaternions H, in the ring M 2 (R) of 2 × 2 square matrices over R and in quaternion algebras over finite fields.

Quadratic formulas for generalized quaternions / Abrate, Marco. - In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS. - ISSN 0219-4988. - ELETTRONICO. - 8:3(2009), pp. 289-309. [10.1142/S0219498809003308]

Quadratic formulas for generalized quaternions

ABRATE, MARCO
2009

Abstract

In this paper we derive explicit formulas for computing the roots of a quadratic polynomial with coefficients in a generalized quaternion algebra over any field F with characteristic not 2. We also give some example of applications for the derived formulas, solving equations in the algebra of Hamilton’s quaternions H, in the ring M 2 (R) of 2 × 2 square matrices over R and in quaternion algebras over finite fields.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2589571
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