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Tuples[{1,-1},5]
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odm=DistanceMatrix[Tuples[{1,-1},5],DistanceFunctionDot]
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MatrixPlot[%]
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hg=Graph[Position[DistanceMatrix[Tuples[{1,-1},5],DistanceFunctionDot],1]]
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hdm=GraphDistanceMatrix[hg]
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MatrixPlot[%]
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odm-hdm
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Case of size 3
Case of size 3
Transitivity
Transitivity
Models of Hilbert Space
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....
This distance was Euclidean distance....
But in Hilbert space, distance is dot product....
But in Hilbert space, distance is dot product....
Comparisons
Comparisons
Approximating Hilbert Space [WRONG]
Approximating Hilbert Space [WRONG]
Distance 1 apart is like sphere packing....
Distance 1 apart is like sphere packing....
E8 lattice ?
E8 lattice ?
Next try
Next try
Non-Flat Hilbert Space
Non-Flat Hilbert Space
Projective 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)
There is a finite-dimensional projective Hilbert space, that has a Kahler metric (CP^n)