The scalar quaternions commute with all other quaternions, that is aq = qa for every quaternion q and every scalar quaternion a. In algebraic terminology this is to say that the field of the scalar …

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

The meaning of QUATERNION is a set of four parts, things, or persons.

Oct 3, 2025 · Quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions. Quaternions and rules for operations on them were invented by Irish …

Aug 20, 2022 · A quaternion contains four components and it is expressed in the form: a+bi+cj+dk, where a, b, c, and d are real numbers, while i, j, and k are unconventional …

Jul 25, 2025 · Quaternions are numbers made up of four parts: one real part and three imaginary parts. They can be written in this form: Here, a is the real part, and b, c, and d are the …

In modern terms, quaternions form a four-dimensional associative normed division algebra over the real numbers, and therefore a ring, also a division ring and a domain. It is a special case of …

Apr 24, 2023 · The most straight-forward way to understand and compute quaternions is from the angle-axis 3D orientation representation. So, we present the math below for how this is done …

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they …

Jul 4, 2023 · A quaternion will cancel out with its Inverse, resulting in the Identity quaternion. Thinking in terms of Axis and Angles, you can view it as negating the axis to point in the …