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Hilbert Book Model Project/Slide S7

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hbmp Hilbert Book Model Project S7

Pairs of quaternions can rotate other quaternions and quaternionic functions

quaternion
norm
spatial part
norm
spatial direction
real part
phase

In multiplication,
quaternions do not
commute.
Thus, in general,

In this multiplication, the imaginary part of that is perpendicular to the imaginary part of

is rotated over an angle that is twice the complex phase of

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