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

a two-dimensional (2D) surface, a projection transformation is applied to the 3D object using a projection matrix. This transformation removes information...

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

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...

Meanwhile, the value projection matrix W V {\displaystyle W^{V}} , in combination with the part of the output projection matrix W O {\displaystyle W^{O}}...

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...

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...

{\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...

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...

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...

backward LSTM layers) are concatenated and multiplied by a linear matrix ("projection matrix") to produce a 512-dimensional representation per input token...

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 ⟹...

In matrix theory, the Frobenius covariants of a square matrix A are special polynomials of it, namely projection matrices Fi(A) associated with the eigenvalues...

{\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} \...

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

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

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

n ) {\displaystyle w\in \mathbf {Gr} (k,\mathbf {R} ^{n})} to the projection matrix P w := ∑ i = 1 k w i w i T , {\displaystyle P_{w}:=\sum _{i=1}^{k}w_{i}w_{i}^{T}...

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...

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...

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...

^{\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...

Theorem (Achlioptas, 2003, Theorem 1.1)—Let the random k × n {\textstyle k\times n} projection matrix R {\textstyle R} have entries drawn i.i.d., either from R i j = {...

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...

the frustum. Together this information can be used to calculate a projection matrix for rendering transformation in a graphics pipeline. Kelvin Sung;...

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