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)