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

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

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

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

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 …

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

In mathematics, the quaternion number system (represented using the symbol ) extends the complex numbers into four dimensions. …

A quaternion of the form 0 + bi + cj + dk, where b; c; d 2 R is called pure imaginary. If q = a + bi + cj + dk is any quaternion, then a is …