Definition talk:Isometry

Is it a fair comment to suggest that there are more similarities than differences between these two definitions? My suggestion is that this page be turned into a master-with-transclusions page rather than pure disambiguation, which I believe better serves terms which have multiple meanings which are genuinely different. --prime mover (talk) 09:20, 11 January 2013 (UTC)

They are genuinely different. The one asks for preserving the inner product, the other for preserving the metric. The difference is substantial, at least from an intuitive point of view. --Lord_Farin (talk) 13:12, 11 January 2013 (UTC)

Just that the page itself says "slightly different". The concept is similar, surely? I always understood the inner product as being a generalisation (under certain assumptions) of the concept of a metric. --prime mover (talk) 14:42, 11 January 2013 (UTC)

Not currently up to speed with my functional analysis. From what I recall the two are not compatible, therefore we should keep them separated. Inner product to me is a wealth of information, much stronger than a metric; it allows to define angles, orthogonality and all sorts of nice results even the generally nice Banach spaces do not attain. --Lord_Farin (talk) 14:46, 11 January 2013 (UTC)

How about moving Definition:Isometry (Hilbert Spaces) to Definition:Unitary Transformation/Hilbert Space or something similar? --abcxyz (talk) 15:56, 11 January 2013 (UTC)

I'm currently busy in the lattice theory department. Do you mind if I get back to this at a later point? --Lord_Farin (talk) 16:05, 11 January 2013 (UTC)

Of course not. --abcxyz (talk) 16:16, 11 January 2013 (UTC)

Read around a bit; unitary transformation is unclaimed as of yet. Unitarity seems to apply to Hilbert spaces only so that Definition:Unitary Transformation is free to hold the concept. Next, it is to be decided if the disambig is to be retained or replaced by "Also defined as" sections. I vote for the former because the notions are still different (even though I now consider Unitary Trafo/Operator to be a natural name for this concept). --Lord_Farin (talk) 21:11, 15 January 2013 (UTC)