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...

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...

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...

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}}...

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...

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...

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 ⟹...

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

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...

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

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

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...

{\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} \...

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}} is the projection of the data onto a lower k-dimensional subspace. Random projection is computationally simple: form the random matrix "R" and project...

position is transformed by the model-view-projection matrix). Because of that, the corresponding texture matrix can be used to "shift" the eye properties...

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...

^{\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...

representation of the head and tail need to be projected using a relational projection matrix on the correct hyperplane of the relation. TransR: A modification...

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...

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}...

\mathbf {P} :=\mathbf {I} -\mathbf {X} _{1}\mathbf {X} _{1}^{+}} is a projection matrix. Following the constrained estimation of β ^ 2 {\displaystyle {\hat...

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...

matrix used in BERT: The three attention matrices are added together element-wise, then passed through a softmax layer and multiplied by a projection...

{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...