3 ms·
Geometric algebra, related to quaternions, can represent Maxwell's equations in a single equation, using polyvectors and the inner and outer products. The suba
by logfromblammo 8y ago
Geometric algebra, related to quaternions, can represent Maxwell's equations in a single equation, using polyvectors and the inner and outer products.
The subalgebras formed by scalar and bivectors (1, x^y, y^z, z^x)--or the monovectors and the pseudoscalar (x, y, z, x^y^z)--from a three-dimensional geometric algebra have a lot of the same mathematical properties as quaternions.
I don't know whether or not octonions have a similar relationship with a 4-D geometric algebra, where one dimension is a timelike dimension, because that is one gnarly mess of anticommutative, nonassociative math to wade through.
- orbifold 8y agoYou can summarize Maxwells equations in any dimension using two formulas: $$ \delta F = j d F = 0 $$ where $F$ is the field-strength two-form and $j$ is the current density.