The Hadamard product is not geometrically meaningful! While it's great for data processing, it doesn't really make sense to compute the Hadamard product of two _spatial vectors_ (i.e. two relative positions in space)
The geometric product makes sense as a product, and so do the inner product and the outer product. You should think of the inner product as a generalized cosine of the angle between two vectors - it measures how much they are pointing in the same direction. And the outer product as a generalized sine of the angle between two vectors - it measures how much they are pointing in directions irrelevant to each other. (both scaled up by the length of the vectors, which is how strongly they are pointing in _any_ direction whatsoever) @dlesnoff Numpy is geared toward arbitrary computation, not geometry in particular. Elementwise operations can be _very_ useful, but not if what you want is to compute rotations, reflections, etc. in space. Elementwise `abs` is very dependent on the basis - if I draw a line on the ground and ask two people to compute its `abs`, the value is going to depend how they drew their x/y axes. But you want something that describes the line _per se_ , not its representation. The 1-norm isn't physical (unless you're PacMan and can't travel diagonally!) It's also why we define `abs` to be the 2-norm on the complex plane (instead of abs(a)+abs(b)*i)
