In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of …

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of …

Mar 14, 2026 · A quaternion is a number with four components: one real part and three imaginary parts. Written out, it looks like q = …

The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton.

Take any unit imaginary quaternion, u = u1i + u2j + u3k. That is, any unit vector.

In H a rotation has an axis (of rotation) and each axis can be represented by a vector so it turns out that each unit pure quaternion …

Oct 10, 2021 · The quaternions, discovered by William Rowan Hamilton in 1843, were invented to capture the algebra of rotations of …

Jul 3, 2026 · Quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions. Quaternions and …

What are quaternions, and how do you visualize them? A story of four dimensions. Describes a way to visualize a hypersphere using …

Quaternions are used to represent rotations. A quaternion is a four-tuple of real numbers {x,y,z,w}. A quaternion is a mathematically …