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In[]:=
Tuples[{1,-1},5]
Out[]=
In[]:=
odm=DistanceMatrix[Tuples[{1,-1},5],DistanceFunctionDot]
Out[]=
In[]:=
MatrixPlot[%]
Out[]=
In[]:=
hg=Graph[Position[DistanceMatrix[Tuples[{1,-1},5],DistanceFunctionDot],1]]
Out[]=
In[]:=
hdm=GraphDistanceMatrix[hg]
Out[]=
In[]:=
MatrixPlot[%]
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In[]:=
odm-hdm
Out[]=

Case of size 3

Transitivity

Models of Hilbert Space

Ternary n-cube:
T(n, 0) = 1, T(n, n) = 2^n, T(n, k) = T(n-1, k-1) + T(n-1, k)

This distance was Euclidean distance....

But in Hilbert space, distance is dot product....

Comparisons

Approximating Hilbert Space [WRONG]

Distance 1 apart is like sphere packing....

E8 lattice ?

Next try

Non-Flat Hilbert Space

Projective Hilbert space

Mod out by projective transformation

There is a finite-dimensional projective Hilbert space, that has a Kahler metric (CP^n)

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