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Unitary in what sense? Clearly multiplication by a unit quaternion preserves the quaternion norm.
by joppy 8y ago
Unitary in what sense? Clearly multiplication by a unit quaternion preserves the quaternion norm.
- edflsafoiewq 8y agoIn the sense of preserving the dot product, x.y = (ux).(uy).
- joppy 8y agoSince the quaternion norm is induced via the quaternion dot product, any transformation that preserves the norm automatically also preserves the dot product. This is a standard result for inner product spaces.
- edflsafoiewq 8y agoAh, polarization? And for it preserving the norm you can use the conjugate. Easy! Thanks!