Definition talk:Orthogonal (Linear Algebra)

("Orthonormal" was there before I got here). So, what do you want me to do with the orthogonal in $\R^n$ part? --GFauxPas 14:12, 20 March 2012 (EDT)

Subsumed Definition:Orthogonal (Hilbert Space) into this page, duplicate pages. I decided not to also make Definition:Orthogonal Subspaces a subpage since it already has its own page, but feel free to change this if you like. Caliburn (talk) 20:39, 27 January 2022 (UTC)

Looks okay from this angle. What we have here is consistent and from what I can tell more or less complete.

Whether we still bother to make a sub-case for Hilbert spaces is possibly worth raising as a question, but if it's exactly the same as the more general linear algebra case, then indeed, probably not worth bothering with.

Again, might as well leave Definition:Orthogonal Subspaces as it is, it's one of those cases where it's a hybrid concept for convenience, to save having to write "orthogonal (closed) linear subspaces" which would be a pain. --prime mover (talk) 21:04, 27 January 2022 (UTC)

Yeah - it'd be analogous to having separate pages for metric spaces and complete metric spaces, most often no point. I don't think we should go beyond splitting up most definitions (that do not require completeness) into Normed Vector Spaces and Inner Product Spaces. (which might be generalised even further when someone eventually comes in to implement general topological vector spaces, (for concepts that only need a topology and not necessarily a norm) but that'll just be built on top of the existing framework rather than replacing anything) Caliburn (talk) 23:06, 27 January 2022 (UTC)