Hilbert Book Model Project/Slide S7

hbmp	Hilbert Book Model Project	S7
	Pairs of quaternions can rotate other quaternions and quaternionic functions
	quaternion ${\color {white}q}$ norm ${\color {white}\lVert q\rVert }$ spatial part ${\color {white}{\vec {q}}}$ norm ${\color {white}{|{\vec {q}}|}}$ spatial direction ${\color {white}{\vec {n}}_{q}={\frac {\vec {q}}{|{\vec {q}}|}}}$ real part ${\color {white}q_{r}}$ phase ${\color {white}q_{\varphi }}$ ${\color {white}q=|q|\exp(q_{\varphi }\,{\vec {n}})}$ In multiplication, quaternions do not commute. Thus, in general, ${\color {white}a\,b/a\neq b}$
	In this multiplication, the imaginary part of ${\color {white}b}$ that is perpendicular to the imaginary part of ${\color {white}a}$ is rotated over an angle that is twice the complex phase ${\color {white}\varphi }$ of ${\color {white}a}$
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