Linguistic Note 4 Grassmann Manifold

 Linguistic Note

 

4

 

Grassmann Manifold

 

 

　　　TANAKA Akio

 

 

Natural number      m, n      m > n

m-dimensional real vector space     R^m

n-dimensional linear subspace  G ^R ( m, n ) is called Grassmann manifold.

m = 2, n = 1     G ^R ( 2, 1 ) = S¹

Generally    G ^R ( m, n ) = G ^R ( m, m-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

www.sekinan.org