Quadratic formulas for split quaternions

Abstract

Unlike the Hamilton quaternion algebra, the split-quaternions contain nontrivial zero divisors. In general speaking, it is hard to find the solutions of equations in algebras containing zero divisor. In this paper, we manage to derive explicit formulas for computing the roots of $x^2+bx+c=0$ in split quaternion algebra.

13 pages

References in corpus (2)

• Split-Quaternions and the Dirac Equation
• Quadratic Split Quaternion Polynomials: Factorization and Geometry

Cited by in corpus (3)

• Quadratic Split Quaternion Polynomials: Factorization and Geometry
• An Algorithm for the Factorization of Split Quaternion Polynomials
• Quadratic Formula: Revisiting a Proof Through the Lens of Transformations