Line Reflections in Geometric Algebra

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From the 2D rotation formula in VGA, we can derive the fundamental GA reflection formula. It reflects one vector across another, creating a line reflection. Because this formula only involves two vectors, it applies in any number of dimensions, even though the derivation was limited to two dimensions!

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Комментарии
Автор

Hey when will you start posting videos of "from 0 to geo" again? I've been waiting for so long. I just wanted to ask.

AnkitKumar-cdfe
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This is equivalent to negative conjugation in SU(2) with Pauli matrices, right?

davidgillies
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This doesn't make sense to me since ((v dot u) v) can only result in a scaled vector v, the result can never be be a vector that is reflected across v.

Also if u and v is perpendicular the result will always be zero.

Or is it another product and not the dot product?

Adeith
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probably a stupid question, because i dont know a lot about algebra, but what is 'vanilla' geometric algebra?

multiarray