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I was wondering if there is such a thing like a Hilbertian affine space. I've seen the definition of an Euclidian affine space, which is:

An affine space (A, V, φ) is an Euclidean affine space if the vector space V is an Euclidean vector space.

Thus, it makes me think that an affine space would be a Hilbertian affine space if the vector space V is a Hilbertian vector space. Is this right? or is there any incompatibility between both spaces (affine and Hilbert spaces)?

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closed as unclear what you're asking by Delta-u, David Hill, max_zorn, Adrian Keister, Thomas Shelby Feb 28 at 2:05

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ I don't know what you mean by "Hilbertian space" $\endgroup$ – David Hill Feb 27 at 18:27