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Ah, I think I was able to think a kind of a visualization myself. You can think of a complex 3-vector as a triplet of labeled points on the complex plane. Scal
by GolDDranks 3y ago
Ah, I think I was able to think a kind of a visualization myself.
You can think of a complex 3-vector as a triplet of labeled points on the complex plane. Scaling this vector by a complex number is equivalent of rotating and scaling this triplet (0 as origin, so no affine transformations).
Therefore, two vectors in this space are equivalent up to a scalar if you can find a complex number that scales/rotates one triplet to another. I can visualize a rotation/scaling transformation of a point cloud on the complex plane pretty well so I'm kind of satisfied this visualization.
- GolDDranks 3y agoAlso, as a neat interpolation between the two vectors, you can think of doing linear interpolation between x := 0 and 1; c1 * c^x where c1 is a complex number component of the first vector and c the complex scalar multiple between the two vectors, rinse and repeat for each component. (Didn't test this in code yet, though) In my mind, this should lead the point cloud of the first vector to spirally slide to form the second vector.