Do Quaternions Form a Field?
The Quaternions Almost Form a Field. They Have the Basic Operations of Addition and Multiplication, and These Operations Satisfy the Associative Laws, (P + Q)...
The quaternions almost form a field. They have the basic operations of addition and multiplication, and these operations satisfy the associative laws, (p + q) + r = p + (q + r), (pq)r = p(qr). ... The only thing missing is the commutative law for the multiplication.
Why are quaternions not a field?
The quaternions form a division algebra. This means that the non-commutativity of multiplication is the only property that makes quaternions different from a field.
Are quaternions a vector space?
Still, the quaternions can be regarded as a four-dimensional vector space formed by combining a real number with a three-dimensional vector, with a basis (set of generating vectors) given by the unit vectors 1, i, j, and k such that i2 = j2 = k2 = ijk = −1.
Alexander Ross has covered the video game industry for a decade, writing deep dives on game design, esports tournaments, VR developments, and gaming culture.
