In statistics, the projection matrix ( P ) {\displaystyle (\mathbf {P} )} , sometimes also called the influence matrix or hat matrix ( H ) {\displaystyle...
13 KB (1,837 words) - 14:54, 22 May 2024
223 A projection matrix that is not an orthogonal projection matrix is called an oblique projection matrix. The eigenvalues of a projection matrix must...
34 KB (5,802 words) - 21:53, 28 April 2024
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These...
32 KB (4,356 words) - 11:34, 19 May 2024
The inversion of the projection matrix P−1, which can be used as the unprojection matrix is defined: P − 1 = [ right − left 2 0 0...
12 KB (1,668 words) - 23:36, 11 March 2024
vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of...
13 KB (1,876 words) - 20:11, 7 June 2024
In computer vision a camera matrix or (camera) projection matrix is a 3 × 4 {\displaystyle 3\times 4} matrix which describes the mapping of a pinhole camera...
12 KB (2,083 words) - 03:23, 28 June 2023
simply by a matrix. However, perspective projections are not, and to represent these with a matrix, homogeneous coordinates can be used. The matrix to rotate...
24 KB (3,826 words) - 19:39, 10 March 2024
Camera resectioning (section Projection)
camera projection matrices of two cameras are used to calculate the 3D world coordinates of a point viewed by both cameras. The camera projection matrix is...
14 KB (2,088 words) - 21:56, 16 April 2024
Moore–Penrose inverse (redirect from Moore-Penrose Matrix Inverse)
{\displaystyle A} is an orthogonal projection matrix, then its pseudoinverse trivially coincides with the matrix itself, that is, A + = A {\displaystyle...
46 KB (7,422 words) - 19:01, 10 June 2024
Cross product (redirect from Cross product matrix)
computer programming. It should not be confused with the dot product (projection product). The magnitude of the cross product equals the area of a parallelogram...
75 KB (11,464 words) - 04:10, 14 April 2024
regression analysis, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables...
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Trace (linear algebra) (redirect from Trace of a matrix)
aii is 1 if the ith point is fixed and 0 otherwise. The trace of a projection matrix is the dimension of the target space. P X = X ( X T X ) − 1 X T ⟹...
36 KB (5,356 words) - 23:46, 9 June 2024
List of named matrices (redirect from List of matrix)
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...
31 KB (1,336 words) - 00:12, 30 November 2023
Graphics pipeline (section Projection)
camera and projection matrix are usually combined into a transformation matrix so that the camera coordinate system is omitted. The resulting matrix is usually...
28 KB (4,397 words) - 13:43, 21 March 2024
Ordinary least squares (redirect from Least-squares normal matrix)
X(XTX)−1XT is the projection matrix onto the space V spanned by the columns of X. This matrix P is also sometimes called the hat matrix because it "puts...
64 KB (8,935 words) - 02:22, 18 May 2024
this method in projection space by representing the above inequality as a determinant of a matrix and applying the projection matrix to it. Another method...
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{\displaystyle C_{n}\,} is an orthogonal projection matrix. That is, C n v {\displaystyle C_{n}\mathbf {v} } is a projection of v {\displaystyle \mathbf {v} \...
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^{\mathsf {T}}\mathbf {X} )^{-1}\mathbf {X} ^{\mathsf {T}}} is the projection matrix (or hat matrix). The i {\displaystyle i} -th diagonal element of H {\displaystyle...
21 KB (3,537 words) - 04:38, 25 April 2024
_{k=1}^{N}\mathbf {W} _{k}\right]}}} Where P j {\displaystyle Pj} is the projection matrix for state m {\displaystyle m} , having elements P j μ ν = δ μ ν δ...
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M_{X_{1}}} projects onto the orthogonal complement of the image of the projection matrix X 1 ( X 1 T X 1 ) − 1 X 1 T {\displaystyle X_{1}(X_{1}^{\mathsf...
9 KB (1,051 words) - 17:38, 2 December 2023
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...
55 KB (10,413 words) - 20:04, 7 June 2024
hidden representations in the linear subspace spanned by a low-rank projection matrix. LoReFT can be seen as the representation-based equivalent of Low-rank...
13 KB (1,378 words) - 02:54, 11 June 2024
This is a list of characters from The Matrix franchise universe. Many of the characters listed here have names reflecting certain aspects of them, such...
35 KB (4,965 words) - 22:34, 27 January 2024
{T} }]y=y^{\operatorname {T} }[I-H]y} , where H is the hat matrix, or the projection matrix in linear regression. The least-squares regression line is...
6 KB (1,055 words) - 08:31, 1 March 2023
N}} is the projection of the data onto a lower k-dimensional subspace. Random projection is computationally simple: form the random matrix "R" and project...
13 KB (1,507 words) - 12:16, 26 March 2024
function is gluOrtho2D which defines a two dimensional orthographic projection matrix. The GLU specification was last updated in 1998, and it depends on...
2 KB (206 words) - 13:05, 22 June 2018
to accommodate those points, accomplished by using a specialized projection matrix. This technique reduces the accuracy of the depth buffer slightly...
16 KB (2,203 words) - 13:32, 28 September 2023
Transpose (redirect from Transpose of a matrix)
transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing...
20 KB (2,525 words) - 12:30, 8 May 2024
In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...
36 KB (4,802 words) - 16:45, 22 May 2024
the point's true projection x {\displaystyle \mathbf {x} } . More precisely, let P {\displaystyle \mathbf {P} } be the projection matrix of a camera and...
2 KB (338 words) - 14:06, 18 December 2023