Quaternion - Wikipedia
The scalar quaternion 1 is the identity element. The scalar quaternions commute with all other quaternions, that is aq = qa for every …
What Is a Quaternion? The Math Behind 3D Rotation
Mar 14, 2026 · A quaternion is a number with four components: one real part and three imaginary parts. Written out, it looks like q = …
Quaternion -- from Wolfram MathWorld
The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for …
Quaternions and spatial rotation - Wikipedia
Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of …
Think of three-dimensional space as being purely imaginary quaternions: R3 = fxi + yj + zk : x; y; z 2 Rg : Just like for complex …
1.2: Quaternions - Mathematics LibreTexts
Oct 10, 2021 · The quaternions, discovered by William Rowan Hamilton in 1843, were invented to capture the algebra of rotations of …
A unit quaternion is a quaternion with norm 1. Note 2.5.1. Note that for a unit quaternion we have qq = q q = 1. Unit quaternions are …
The set of unit quaternions is closed under quaternion multiplication, because the norm of the product of quaternions is the product …
Quaternion - Simple English Wikipedia, the free encyclopedia
In mathematics, the quaternion number system (represented using the symbol ) extends the complex numbers into four dimensions. …
Quaternion | Rotations, Hypercomplex Numbers, Algebra | Britannica
Jul 3, 2026 · Quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions. Quaternions and …