Talk:Transformation matrix

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 Field:  Algebra

Preferred notation for discussion[edit]

Is it the purpose of this discussion to have only mathematicians talk to other mathematicians? I come from a programming background and am getting into 3D transformations. (Not a mathematician.) I cannot read the first paragraph. In the second sentence Rn (Rn] and Rm are used. In most programming languages that is an error as both are undefined.MartinRinehart (talk) 21:30, 25 November 2009 (UTC)

My friend, frankly, most mathematicians are not actual mathematicians, but retarded drones. They express things like you see in this article, because they themselves don’t understand the whys. They never learned it. They just know it by heart. Real mathematics comes from a problem that people once tried to solve. Then it evolved, so that it could solve other problems. Until it reached a very generalized form. This form then is “taught” (more hammered in) without any origins and reasonings, and without allowing any questioning on “the holy rules”. And real mathematicians hate this, because it is the exact opposite of what math is all about. If you want to really learn math, in a way that allows to come up with things on your own, because you get it… deeply and fully… then I recommend reading the book that Paul Lockhart will bring out when he’s done with writing it. Which is written to counter those horrible failures of drone pseudo-mathematicians. — (talk) 00:28, 21 August 2010 (UTC)
The second sentence says the same as the first sentence in a more formal way. You could have just followed the links to or looked up a term you don't understand. This is standard notation, what notation would you use instead? (talk) 14:34, 3 September 2014 (UTC)

Affine matrix question[edit]

Does anyone know if it is possible to extract information from an affine matrix? Say you have a matrix rotated by 180 degrees and skewed on the X axis can you extract those two pieces of information? -- 16:29, 24 May 2006 (UTC)

yeah! there are various techniques to decompose a transformation matrix into one rotate, one translate and two shear operations. --Diego 13:58, 19 June 2006 (UTC)


I don't have the time to edit it, but someone should edit the section about the transformation matrix for a reflection. The version they have is fine for a line from the origin to (ux,uy), but in many cases it's easier to do it as a reflection in the line y = x tan q. The matrix would be [[cos 2q sin 2q] [sin 2q -cos 2q]] (...I think).

2D rotation matrix error[edit]

Someone please check the 2D rotation matrix. I believe the signs on the sin()'s are backwards for clockwise/counterclockwise rotation... TiBaal89 (talk) 18:36, 3 September 2008 (UTC)

Please suggest an authentic source for coordinate transformation. There is a sign change required. — Preceding unsigned comment added by Share'n'serve (talkcontribs) 10:51, 4 October 2013 (UTC)

From what I can tell, the clock-wise and anti-clockwise rotations being presented are correct. However, it is not necessary to include both, clock-wise rotations are simply anti-clock wise rotations by a negative angle. Since sine and cosine are defined for all of the real numbers (and all possible angles) it's not necessary include both kinds of rotations. I recommend removing the clock-wise rotation, since mathematically positive rotation is counter-clockwise according to the definition of sine and cosine. — Preceding unsigned comment added by (talk) 20:06, 13 July 2014 (UTC)

Error in the Perspective Projection Section[edit]

The matrix in the section on perspective projection is wrong. It's just the identity matrix. :) I think the bottom row should have been "0 0 1 0" instead of "0 0 0 1". Right? (sorry, i'm new to wikipedia, don't feel comfortable enough to change articles yet) Zaippa (talk) 04:15, 20 September 2008 (UTC)

Ok, i fixed the error here a day later.. Now the matrix actually does what it says in the text :) (seems that the matrix was correct some edits ago, but someone came along and changed it into the identity matrix) Zaippa (talk) 16:37, 20 September 2008 (UTC)

This is how the transforms look when calculated symbolically in MathCad:


To be consistent with the text, clearly the first of these two should be used. HonestGent (talk) 07:47, 17 May 2010 (UTC)

I think there is also another error. If we are mapping onto z = h, then the number in the bottom row should be -1/h. In this case -1. I am posting here because I'm not really sure, so somebody who knows should fix this.My source.-- (talk) 14:49, 26 November 2008 (UTC)


I believe that this the clockwise and counterclockwise examples are opposite of the matrixes. (talk) 20:41, 20 September 2008 (UTC)

FEB 2014: The pair of rotation matrices suddenly appears twice - (supposedly CW, CCW, but actually both CCW), the second set is correct. — Preceding unsigned comment added by 2620:104:E001:9030:AD41:42DB:96B0:860E (talk) 14:58, 18 February 2014 (UTC)


I believe the first reflection matrix given in is not correct. Here I expose a correct statement for replacement:

"To reflect a vector about a line that goes through the origin, let (nx, ny) be a *unit* vector in the direction of the line:


Nevertheless, I don't want to erase current work because my arguments are heuristics, not matematics ;)... I'm not a matematician but a software developer. I tried to use current transformation matrix in a program and didn't work. The given one is correct and can be easily derived from equation (2) of

Hope that somebody (more indicated than me) can correct the problem.

greetings from Uruguay,

Sebastián Gurin —Preceding unsigned comment added by Cancerbero sgx (talkcontribs) 16:33, 3 August 2009 (UTC)


As I understand it, translation is a liner transformation. As such, does it have an associated matrix form? Either way, I'd like to see this explained in the article. — Cheers, Steelpillow (Talk) 13:04, 12 December 2010 (UTC)

The first sentence of this article basically says it, though you'll have to have some knowledge of linear algebra to understand it. Simply put, a linear transformation is a matrix. And any matrix can be used to execute a linear transformation. When you multiply a vector with a matrix, the matrix is the linear transformation from the first vector, into the resulting vector. -- (talk) 20:40, 10 January 2011 (UTC)
Translation is not a linear transformation, as it does not preserve scalar multiplication of vectors and vector addition. This means that a n-D translation cannot be represented by a n-by-n matrix. See Transformation matrix#Uses. Paolo.dL (talk) 13:46, 15 February 2012 (UTC)

Other language links[edit]

The other language links lead to pages (e.g. in Russian, Ukrainian, French) which discuss change of basis matrices rather than general transformation matrices, although some of them go into 2D/3D graphics later on. Maybe the links should be changed accordingly? --ToastieIL (talk) 00:57, 24 September 2011 (UTC)

Homogeneous transformation matrix[edit]

4x4 transformation matrices containing 4-D homogeneous coordinates are widely used to perform non-linear (affine and projective) transformations of vectors in 3-D space. These transformations become linear when represented in 4-D, using homogeneous coordinates. The expression "homogeneous transformation matrix" is widely and rather conventionally used by many experts in computer graphics, robotics, biomechanics, to indicate these matrices. However, these matrices are used to perform transformations that are non-homogeneous in 3-D. They are frequently used, for instance, to represent roto-translation, a composition of translation and rotation. In this specific case, their proper name is, as suggested in the article, affine transformation matrices.

Since the misleading expression "homogeneous transformation matrix" is widely used, and the internal link Homogeneous transformation matrix redirects to Transformation matrix#Uses, I think it would be wise to shortly discuss it in the article.

Notice that all linear transformations are by definition "homogeneous", as they must preserve, by definition, the results of scalar multiplication (see homogeneous function):

(homogeneity of degree 1)

On the contrary, a non-linear transformation may be non-homogeneous. Translation and roto-translation, for instance, are non-homogeneous.

NOTE : This topic was briefly discussed elsewhere.

Paolo.dL (talk) 13:42, 15 February 2012 (UTC)


PLEASE TELL ME THE INBRIEF DESCRIPTION OF TH E X-SHEARIN G./................ — Preceding unsigned comment added by (talk) 15:04, 28 August 2012 (UTC)

History of..?[edit]

I e-searched in for some hot History of Transformation Matrices action; it's not above the fold! ~~Phlip 2014 — Preceding unsigned comment added by (talk) 22:52, 13 June 2014 (UTC)

Article content vs Computer science[edit]

I find it little bit confusing that all examples in this and related pages, even those talking about 2D/3D gaming applications, refer to affine matrices where translation coordinates appear on the 3rd column. This examples use a column vector to represent a point. However, in computer graphics, the 1st dimension is X, horizontal, thus 1-dimentional array is represented as a row vector. As a consequence, the translation values Tx and Ty actually are located in the 3rd row of affine matrix 3*3, NOT the 3rd column. This makes all the examples inapplicable to real-life computer graphics. See examples: Windows GDI, WPF and even MAC. The last link generally is platform-independent, about MP4 files. --2A02:1812:1110:C00:7C25:DF6D:3CD7:4C7F (talk) 22:00, 18 April 2015 (UTC)

Error in Examples in 3D Computer Graphics section[edit]

There is an obvious error in the section. The first subject there is Rotation. I can't be certain what the author meant by rotating an angle, but it is nonsense as presented.
The general rotation in 3D about an axis gives you a cone. If it is restricted to a given distance from the origin, then you have a circle. It is not possible to rotate a point in 3D into another point given a single angle without additional assumptions as to the direction of rotation. The same is true for the rotation of a line. (talk) 22:25, 21 April 2017 (UTC)