Why Are Quaternions 4D?
The Reason That the Dimensions Are in Geometric Progression 1, 2, 4, 8 Is That They Can Be Derived from Repeatedly Applying the Cayley-Dickson Construction...
The reason that the dimensions are in geometric progression 1, 2, 4, 8 is that they can be derived from repeatedly applying the Cayley-Dickson construction, which doubles the dimension at each step. This explains the absence of dimension 3.
Why do quaternions have 4 numbers?
"A quaternion is basically an axis in 3D space with a angle of rotation around the axis. Four values make up a quaternion, namely x, y, z and w. Three of the values are used to represent the axis in vector format, and the forth value would be the angle of rotation around the axis."
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Is a quaternion a 4D vector?
The quaternions are a four dimensional vectorspace over the reals. However, being a "4D vector" is more than just having four components. Being part of a vectorspaces says something about how you can interact with other things. Two vectors may be added.
Marcus Vance is a cybersecurity auditor and technology writer dedicated to educating the public about online safety, data privacy regulations, enterprise security, and emerging cyber threats.
