Rotor (mathematics) | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Rotor_(mathematics)


00:00:30 1 Generation using reflections
00:00:46 1.1 General formulation
00:01:17 1.2 Restricted alternative formulation
00:01:48 1.3 Rotations of multivectors and spinors
00:02:18 2 Homogeneous representation algebras
00:02:49 3 See also



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SUMMARY
=======
A rotor is an object in geometric algebra (or more generally Clifford algebra) that rotates any blade or general multivector about the origin. They are normally motivated by considering an even number of reflections, which generate rotations (see also the Cartan–Dieudonné theorem).
The term originated with William Kingdon Clifford, in showing that the quaternion algebra is just a special case of Hermann Grassmann's "theory of extension" (Ausdehnungslehre).  Hestenes defined a rotor to be any element 
  
    
      
        R
      
    
    {\displaystyle R}
   of a geometric algebra that can be written as the product of an even number of unit vectors and satisfies 
  
    
      
        
          
            
              R
              ~
            
          
        
        R
        =
        1
      
    
    {\displaystyle {\tilde {R}}R=1}
  , where 
  
    
      
        
          
            
              R
              ~
            
          
        
      
    
    {\displaystyle {\tilde {R}}}
   is the "reverse" of 
  
    
      
        R
      
    
    {\displaystyle R}
  —that is, the product of the same vectors, but in reverse order.