Hilbert Book Model Project/Slide S7

hbmp	Hilbert Book Model Project	S7
	Pairs of quaternions can rotate other quaternions and quaternionic functions
	Template:Center top quaternion $q$ norm $\Vert q\Vert$ spatial part $\overrightarrow{q}$ norm $|\overrightarrow{q}|$ spatial direction ${\overrightarrow{n}}_q=\frac{\overrightarrow{q}}{|\overrightarrow{q}|}$ real part $q_r$ phase $q_{\phi }$ $q=|q|\exp (q_{\phi }\overrightarrow{n})$ Template:Center top Template:Center bottom Template:Center top In multiplication, quaternions do not commute. Thus, in general, $ab/a\ne b$ Template:Center bottom
	In this multiplication, the imaginary part of $b$ that is perpendicular to the imaginary part of $a$ is rotated over an angle that is twice the complex phase $\phi$ of $a$
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