In statistics, the projection matrix ( P ) {\displaystyle (\mathbf {P} )} , sometimes also called the influence matrix or hat matrix ( H ) {\displaystyle...

223  A projection matrix that is not an orthogonal projection matrix is called an oblique projection matrix. The eigenvalues of a projection matrix must...

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...

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...

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...

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...

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...

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...

{\displaystyle A} is an orthogonal projection matrix, then its pseudoinverse trivially coincides with the matrix itself, that is, A + = A {\displaystyle...

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...

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 ⟹...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

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...

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...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

camera and projection matrix are usually combined into a transformation matrix so that the camera coordinate system is omitted. The resulting matrix is usually...

^{\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...

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...

{\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} \...

_{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...

function is gluOrtho2D which defines a two dimensional orthographic projection matrix. The GLU specification was last updated in 1998, and it depends on...

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...

the point's true projection x {\displaystyle \mathbf {x} } . More precisely, let P {\displaystyle \mathbf {P} } be the projection matrix of a camera and...

{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...

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...

1. Moreover, the matrix vwT is the projection onto the eigenspace corresponding to r. This projection is called the Perron projection. Collatz–Wielandt...

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...

h {\displaystyle {i}^{th}} diagonal element of the ortho-projection matrix (a.k.a hat matrix) H = X ( X ⊤ X ) − 1 X ⊤ {\displaystyle \mathbf {H} =\mathbf...

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...

covariants of A, which are (projection) matrix Lagrange polynomials of A. Sylvester's formula applies for any diagonalizable matrix A with k distinct eigenvalues...