Python code I can incorporate into a Jupyterlab notebook.
The code must be general enough that I can pass in the # of dimensions, and get back some sort of rotation matrix (?) that I can multiply the original data array by to get the transformed coordinates for each row.
Bonus points for allowing a variable amount of rotation (the rotation angle), though I expect only to use 45% for each dimension. There is no need to rotate dimensions at different angles.
I need an expert in computational geometry to solve the following problem.
I have an array of data where each row represents coordinates of a single point in a high dimensional space (700+ dimensions).
I need to rotate ALL the axes 45%, resulting in (700+) new coordinates for each point.
I can find examples in 2 and 3 dimensions, but nothing more general, using "Hamilton’s quaternions" and "Euler angles".
I'm not knowledgeable enough in computational geometry to tackle this task. I know that the rotation can be achieved through a series of "simple" (planar?) rotations, but I'm unclear if all such rotation sequences result in the same final answer (commutativity), how many rotations I would need, and I don't know how to define such simple rotations in a hyperspace. In any case, I suspect there's a much better way to get the final rotation matrix in a single shot.
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