Talk:Projection matrix

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This opening sentence seems weird:

The hat matrix, H, is used in statistics to relate errors in residuals to experimental errors.

I'm going to think about how to rephrase it. Michael Hardy (talk) 22:50, 12 January 2008 (UTC)Reply

I've just done that and rewritten the article to leave the use of H in formulae to do with errors to later, and changed to more standard notation for linear models as used in other Wikipedia entries. Qwfp (talk) 15:26, 10 September 2008 (UTC)Reply

The wikilink operator matrix redirects here, but this term is not mentioned. Is this meant to be the same as the hat matrix, or is it some other combination of matrices that appear here? This particular wikilink is presently accessed from Mean squared prediction error. Melcombe (talk) 12:39, 26 October 2010 (UTC)Reply

Since operator is the same as transformation in linear algebra, it is natural to expect that "operator matrix" should redirect to transformation matrix. --Javalenok (talk) 20:26, 2 January 2013 (UTC)Reply

I think it would be useful to have a section about some basic characteristics of the hat matrix, such as the fact that this matrix ix symmetric and ${\displaystyle H^{2}=H}$.--91.138.154.198 (talk) 21:21, 2 February 2011 (UTC)Reply

It already includes this: "The hat matrix corresponding to a linear model is symmetric and idempotent, that is, H² = H." Qwfp (talk) 21:34, 2 February 2011 (UTC)Reply

It is stated that the hat matrix has a number of useful properties, but none of them are given -- why state this but not give any examples? Further, at least one of the two citations (Draper) given at this point doesn't appear to mention any properties of the hat matrix that I can see. This part should either be elaborated on, or removed. — Preceding unsigned comment added by 193.60.86.172 (talk) 16:46, 20 January 2014 (UTC)Reply

Maybe I'm seeing this through the econometrics lense, but I'm off the impression that ${\displaystyle \mathbf {X} (\mathbf {X} ^{\mathsf {T}}\mathbf {X} )^{-1}\mathbf {X} ^{\mathsf {T}}}$ is more often referred to as "projection matrix" rather than "hat matrix." Most notable in Amemiya (1985), Advanced Econometrics, and Hayashi (2000), Econometrics, two of the most influential graduate-level econometrics textbooks. Should we re-name this article? --bender235 (talk) 22:04, 20 December 2015 (UTC)Reply

Also, compare the title for rotation matrix performing a rotation. The projection matrix is performing a projection. --bender235 (talk) 00:27, 24 March 2016 (UTC)Reply