四元数是简单的超复数。 复数是由实数加上虚数单位 i 组成，其中i^2 = -1。 相似地，四元数都是由实数加上三个虚数单位 i、j、k 组成，而且它们有如下的关系： i^2 = j^2 = k^2 = -1， i^0 = j^0 = k^0 = 1 , 每个四元数都是 1、i、j 和 k 的线性组合，即是四元数一般可表示为a + bk+ cj + di，其中a、b、c 、d是实数。

对于i、j、k本身的几何意义可以理解为一种旋转，其中i旋转代表X轴与Y轴相交平面中X轴正向向Y轴正向的旋转，j旋转代表Z轴与X轴相交平面中Z轴正向向X轴正向的旋转，k旋转代表Y轴与Z轴相交平面中Y轴正向向Z轴正向的旋转，-i、-j、-k分别代表i、j、k旋转的反向旋转(The four element number is a simple super complex number. The complex is composed of real and imaginary unit of I, where i^2 = -1. Similarly, the number of four yuan is composed of real and three imaginary unit of I, J, K, and they have the following relationship: i^2 = j^2 = k^2 = -1, i^0 = j^0 = k^0 = 1, four yuan each number is a linear combination of 1, I, J and K, i.e. the number is four yuan in general can be expressed as a + bk+ CJ + Di, B, C, a, D is a real number.
For I, J, K geometric meaning itself can be understood as a rotation, which represents the X I rotation axis and Y axis plane intersecting the positive X axis to the positive Y axis rotation, J rotation represents the Z axis and X axis plane intersecting the positive Z axis to the positive X axis rotation, K rotation Y axis intersects the Z axis in the plane of the positive Y axis to the positive Z axis rotation, -i, -j, I, J and -k respectively represent the K rotation and reverse rotation)