Hypercomplex numbers {quaternion} can be scalar plus three-dimensional vector: a + b*i + c*j + d*k, where a, b, c, and d are real numbers, and i, j, and k are orthogonal unit vectors.
operations
Quaternion addition is like translation. Multiplying quaternions is non-commutative: i*j = k, j*k = i, k*i = j, j*i = -k, k*j = -i, i*k = -j and describes quaternion rotations. Quaternions can divide.
space
Complex numbers map to two-dimensional space, and quaternions map to three-dimensional space.
spinor
Real-number spinors represent rotating quaternions.
Mathematical Sciences>Number Theory>Number Types>Complex Number>Hypercomplex
3-Number Theory-Number Types-Complex Number-Hypercomplex
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Date Modified: 2022.0224