Talk:Congruent transformation

Congruent transformation

Hi. You recently created the article congruent transformation. I'm afraid that I don't quite understand it. First of all, the definition (transformations of the form $x\mapsto D^{\mathrm{\top }}xD$) does not include translations, but the last sentence about triangle implies that translations are included. Secondly, if one takes

$D=\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$

then the transformation is not an isometry. Could you please clarify? Arigatō, Jitse Niesen (talk) 23:09, 11 August 2005 (UTC)

Thanks for info. Actually I knew the problem. I copied the definition from mathworld verbatimly, as I couldn't find a good one. I am putting a corrected version and clarifying if reflections are allowed or not. -- Taku 23:19, August 11, 2005 (UTC)

Is n supposed to be the dimension of the space? It needs to say what n is. Michael Hardy 01:17, 13 August 2005 (UTC)

This article is incorrect

This article is incorrect. There are two meanings to congruent transformation, one is an isometry (distance preserving map) and the other is a transformation of the form D^TnD. These two have nothing in common. The mathworld article made it clear, while the person who wrote this article thought that they are all and the same. Oleg Alexandrov 01:42, 13 August 2005 (UTC)

Besides, that is not n, that is η — a matrix, and we are talking about a map η → D^TηD mapping a matrix to a matrix. Oleg Alexandrov 01:46, 13 August 2005 (UTC)

I am turing this into a disambig page, as isometry already describes the first sense. I didn't know about the second sense. -- Taku 02:32, August 13, 2005 (UTC)