realquaternion
Realquaternion is a term used to describe the quaternion algebra over the real numbers. In this context, a realquaternion is an element q = a + bi + cj + dk, where a, b, c, and d are real numbers and the units i, j, k satisfy the relations i^2 = j^2 = k^2 = ijk = -1, with ij = k, ji = -k, and cyclic permutations. This establishes a four-dimensional real vector space with a non-commutative multiplication.
The realquaternions form a real associative division algebra, often denoted H. Key operations include the conjugate
Unit realquaternions, those with N(q) = 1, correspond to rotations in 3D. They can be used to encode
Applications of realquaternions are widespread in computer graphics, robotics, aerospace, and simulation, where robust handling of