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 $$ x \mapsto D^\top x D$$) does not include translations, but the last sentence about triangle implies that translations are included. Secondly, if one takes
 * $$ D = \begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix} $$

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 DTnD. 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 &eta; &mdash; a matrix, and we are talking about a map &eta; &rarr; DT&eta;D 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)