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Hilbert Book Model Project/Slide 5

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hbmp Hilbert Book Model Project 5

This special version of the number system acts as a
background parameter space

A special reference operator of the separable Hilbert space uses the rational values of this version of the quaternionic number system to enumerate the members of an orthonormal base of the Hilbert space and uses them as its eigenvectors and uses the enumerators as the corresponding eigenvalues

Other reference operators use other versions of the number system
and generate parameter spaces as their eigenspaces
that float on top of the background parameter space

These parameter spaces serve floating platforms

The platform uses a private version of the number system, thus the inner product also uses that version

This means that the floating platform represents a private Hilbert space

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