Definition talk:Orthonormal Basis

The original page had defined an orthonormal basis on a general vector space over a general field.

This is unsound, as it requires that the vector space actually be a normed vector space, which in turn requires that the field in question be a valued field, that is, has a norm on it.

Hence the definition (unsourced as it was) has been reversed out. The definition Definition:Orthonormal Basis of Vector Space has been transcluded, in order to allow this concept to be applied to other structures.

For example, we also note that there is a request to merge Definition:Basis (Hilbert Space) into this page as well, which is also under consideration. --prime mover (talk) 09:41, 12 January 2023 (UTC)


 * Yes, we should not assume the finite dimensionality in this definition. Or, need to create a separate page for an abstract vector space with inner product, that is not necessarily finite dimensional. --Usagiop (talk) 21:20, 29 May 2023 (UTC)