Multivector | Wikipedia audio article
Channel: wikipedia tts
Date: 10/05/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Multivector


00:01:40 1 Wedge product
00:01:57 2 Area and volume
00:04:44 2.1 Multivectors in Rsup2/sup
00:05:43 2.2 Multivectors in Rsup3/sup
00:08:17 3 Grassmann coordinates
00:14:35 3.1 Multivectors on iP/isup2/sup
00:15:37 3.2 Multivectors on iP/isup3/sup
00:15:48 4 Clifford product
00:15:54 5 Geometric algebra
00:16:04 5.1 Examples
00:16:20 5.2 Bivectors
00:18:36 6 Applications
00:22:34 7 See also
00:22:54 8 References
00:27:32 1 is the set of points x
00:32:22 1 with the plane x
00:45:25 Clifford product
00:49:52 Geometric algebra
00:51:41 Examples
00:52:40 Bivectors
00:55:18 Applications
00:55:37 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.9049529929004138
Voice name: en-GB-Wavenet-D


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In multilinear algebra, a multivector, sometimes called Clifford number, is an element of the exterior algebra Λ(V) of a vector space V. This algebra is graded, associative and alternating, and consists of linear combinations of simple k-vectors (also known as decomposable k-vectors or k-blades) of the form

  
    
      
        
          v
          
            1
          
        
        ∧
        ⋯
        ∧
        
          v
          
            k
          
        
        ,
      
    
    {\displaystyle v_{1}\wedge \cdots \wedge v_{k},}
  where 
  
    
      
        
          v
          
            1
          
        
        ,
        …
        ,
        
          v
          
            k
          
        
      
    
    {\displaystyle v_{1},\ldots ,v_{k}}
   are in V.
A k-vector is such a linear combination that is homogeneous of degree k (all terms are k-blades for the same k). Depending on the authors, a "multivector" may be either a k-vector or any element of the exterior algebra (any linear combination of k-blades).In differential geometry, a k-vector is a k-vector in the exterior algebra of the tangent vector space; that is, it is an antisymmetric tensor obtained by taking linear combinations of the wedge product of k tangent vectors, for some integer k ≥ 0. A k-form is a k-vector in the exterior algebra of the dual of the tangent space, which is also the dual of the exterior algebra of the tangent space.
For k = 0, 1, 2 and 3, k-vectors are often called respectively scalars, vectors, bivectors and trivectors; they are respectively dual to 0-forms, 1-forms, 2-forms and 3-forms.