Monday 5 January 2015

Linguistic Note 4 Grassmann Manifold / July 21, 2007

Linguistic Note

4

Grassmann Manifold


   TANAKA Akio


Natural number      mn      n
m-dimensional real vector space     Rm
n-dimensional linear subspace  G R ( mn ) is called Grassmann manifold.
m = 2, n = 1     G R ( 2, 1 ) = S1
Generally    G R ( mn ) = G R ( mm-n )
[Note]
Now 2 dimensions express <space> dimension and <time> dimension, S1 expresses 1 dimensional spacetime by circumference.
[Reference]
Cell Theory     From Cell to Manifold     Tokyo June 2, 2007

Tokyo July 21, 2007
Sekinan Research Field of Language

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