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Quaternion multiplication table ↓ × → 1 i j k; 1: 1: i: j: ... 1 if and only if it is a vector quaternion with norm 1. By definition, the set of all such vectors ...
Multiplication table of quaternion group as a subgroup of SL(2,C). The entries are represented by sectors corresponding to their arguments: 1 (green), i (blue), −1 (red), − i (yellow). The two-dimensional irreducible complex representation described above gives the quaternion group Q 8 as a subgroup of the general linear group GL ( 2 ...
One possible multiplication table is described in the Multiplication table section, but it is not unique. [5] Unlike three dimensions, there are many tables because every pair of unit vectors is perpendicular to five other unit vectors, allowing many choices for each cross product.
The multiplication of quaternions is non-commutative. This fact explains how the p ↦ q p q −1 formula can work at all, having q q −1 = 1 by definition. Since the multiplication of unit quaternions corresponds to the composition of three-dimensional rotations, this property can be made intuitive by showing that three-dimensional rotations ...
Multiplication of a scalar and a vector was accomplished with the same single multiplication operator; multiplication of two vectors of quaternions used this same operation as did multiplication of a quaternion and a vector or of two quaternions.
In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the ...
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