I am programming a basic mathematical library that deals with vectors, matrices, tensors, holors, functions, etc. I am wondering what the best terminology will be regarding pointwise/componentwise/etc operations (or maybe I should even call the componentwise matrix product a Hadamard product). Are any of those terms more accurate/preferable when talking about vectors, matrices, holors, functions etc?
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When talking vectors/matrices/tensors it is best to avoid point-wise because it is decently ambiguous since vectors can be interpreted as points, so a point-wise multiplication might just be some inner product. I would go with component-wise for most vector operations even for the Hadamard product, since matrix libraries are often used by people who don't know about the Hadamard product but still might want to multiple matrices component-wise it can be easier to understand.
When discussing functions everything is usually defined to be point-wise, this is because generally speaking function operations are local. For example to calculate f(5) * g(6) you don't need to know anything about the two functions other than their values at these points.
Sam
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What about elementwise and coordinatewise? – lightxbulb Jul 08 '19 at 22:02
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1Element-wise is equivalent to component-wise, I have never actually heard of coordinate-wise but its probably interchangeable with point-wise. – Sam Jul 09 '19 at 15:05