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2. Quaternion group - Wikipedia

   en.wikipedia.org/wiki/Quaternion_group

   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 ...

3. Quaternion - Wikipedia

   en.wikipedia.org/wiki/Quaternion

   For two elements a 1 + b 1 i + c 1 j + d 1 k and a 2 + b 2 i + c 2 j + d 2 k, their product, called the Hamilton product (a 1 + b 1 i + c 1 j + d 1 k) (a 2 + b 2 i + c 2 j + d 2 k), is determined by the products of the basis elements and the distributive law. The distributive law makes it possible to expand the product so that it is a sum of ...

4. Seven-dimensional cross product - Wikipedia

   en.wikipedia.org/wiki/Seven-dimensional_cross...

   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.

5. Classical Hamiltonian quaternions - Wikipedia

   en.wikipedia.org/wiki/Classical_Hamiltonian...

   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.

6. Quaternions and spatial rotation - Wikipedia

   en.wikipedia.org/wiki/Quaternions_and_spatial...

   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 ...

7. Vector multiplication - Wikipedia

   en.wikipedia.org/wiki/Vector_multiplication

   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 ...