Grassmann Language
TANAKA Akio
1.
is (N+1) dimensional complex space.
is Grassmann manifold that is all the spaces which are made from (k+1) dimensional linear subspace of 
.
Element of (k+1) dimensional exterior space 
of 
is called (k+1) vector.
Elements of is given by (k+1) vector of decomposable is givenby the below.
.
is one fixed base of .
is also able to written.
is called Cayley-Plücker-Grassmann coordinates.
is unitary group.
.
.
Hermitian inner product is defined as the below.
.
.
is called norm of 
.
Over 
.
.
.
.
.
.
Kähler form is
.
The upper measuring is Kähler measuring.
.
.
2.
(Theorem)
Grassmann manifold has invariant Kähler measuring by operation of .
Its Kähler form is equal to 
times of hyperplane section bundle's curvature form over 
that is determined by immersion of Cayley-Plücker-Grassmann coordinates and hermitian norm 
.
3.
Grassmann language model is supposed as the below.
Word is expressed by grassmann manifold.
Word has location and distance, that are expressed by Cayley-Plücker-Grassmann coordinates and hermitian norm .
4.
References are below.
<On distance of word>
Distance Theory /Tokyo May 5, 2004
Distance of Word / Complex Manifold Deformation Theory / Tokyo November 30, 2008
<On manifold>
From Cell to Manifold/ Cell Theory / June 2, 2007
[ Cell Theory / Continuation of Quantum Theory for Language / For LEIBNIZ and JAKOBSON ]
Tokyo
March 6, 2012
Sekinan Research Field of Language
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