In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 [1][2] and applied …

A spatial rotation around a fixed point of radians about a unit axis (,,) that denotes the Euler axis is given by the quaternion (,,,), where = ⁡ (/) and = ⁡ (/).

Quaternions are very efficient for analyzing situations where rotations in R3 are involved. A quaternion is a 4-tuple, which is a more concise representation than a rotation matrix. Its geo …

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.

• To present better ways to visualize quaternions, and the effect of quaternion multiplication on points and vectors in 3-dimensions. • To develop simple, intuitive proofs of the sandwiching …

2021年10月10日 · The quaternions, discovered by William Rowan Hamilton in 1843, were invented to capture the algebra of rotations of 3-dimensional real space, extending the way …

2025年3月20日 · quaternion, in algebra, a generalization of two-dimensional complex numbers to three dimensions. Quaternions and rules for operations on them were invented by Irish …

A quaternion is an expression of the form: We extend addition, subtraction and multiplication to the quaternions by obey-ing the above rules as well as distributivity and associativity. The set …

Quaternions are a four-dimensional number system that is an extension of the field of complex numbers. Multiplication of quaternions is non-commutative in that the order of elements …