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it shouldn't be an either or with geometry and algebra. both are valid and it helps to know both. representing H as a matrix is certainly valid and makes comput
by gmadsen 8y ago
it shouldn't be an either or with geometry and algebra. both are valid and it helps to know both. representing H as a matrix is certainly valid and makes computations easier, but I dont really think that is building intuition
- earthicus 8y agoThe modern approach is not lacking all geometry, and the 19th century presentation is not lacking all algebra. Any respectable treatment will include both, the question is which makes the relationship clearer? The abstract algebraic approach talks of 'the rotation group' which maps on to geometric concepts as cleanly and directly as possible. Then we talk of different parameterizations or representations of this group, with the unit quaternions being the 'double cover' of the rotation group (which gives rise to the primary difficulty in understanding them - that a rotation by 360 degrees reverses orientation, and 720 degrees returns us to where we started). I think the modern approach is much clearer - the geometric ideas appear more directly, and the algebra is far less messy.
- edflsafoiewq 8y ago> I think the modern approach is much clearer - the geometric ideas appear more directly, and the algebra is far less messy. Can you show us an example?