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searching for Projection matrix 48 found (69 total)

Projection (linear algebra) (5,806 words) [view diff] exact match in snippet view article

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

Camera resectioning (2,251 words) [view diff] exact match in snippet view article find links to article

camera. Usually, the camera parameters are represented in a 3 × 4 projection matrix called the camera matrix. The extrinsic parameters define the camera

OpenGL Utility Library (206 words) [view diff] exact match in snippet view article find links to article

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

Object locative environment coordinate system (134 words) [view diff] exact match in snippet view article find links to article

screen objects to 2D coordinates using the camera position (using a projection matrix) and uses these coordinates to impart movement constraints to the

Sylvester's formula (1,118 words) [view diff] no match in snippet view article find links to article

_{j}I\right)} are the corresponding Frobenius covariants of A, which are (projection) matrix Lagrange polynomials of A. Sylvester's formula applies for any diagonalizable

Projective texture mapping (587 words) [view diff] exact match in snippet view article find links to article

the object space vertex position is transformed by the model-view-projection matrix). Because of that, the corresponding texture matrix can be used to

Camera matrix (2,083 words) [view diff] exact match in snippet view article find links to article

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

Drazin inverse (856 words) [view diff] exact match in snippet view article find links to article

equivalently, by the properties AA#A = A, A#AA# = A#, and AA# = A#A. A projection matrix P, defined as a matrix such that P2 = P, has index 1 (or 0) and has

Reprojection error (338 words) [view diff] exact match in snippet view article find links to article

{x} } . More precisely, let P {\displaystyle \mathbf {P} } be the projection matrix of a camera and x ^ {\displaystyle {\hat {\mathbf {x} }}} be the image

Vector projection (1,718 words) [view diff] exact match in snippet view article find links to article

represented by a projection matrix. To project a vector onto the unit vector a = (ax, ay, az), it would need to be multiplied with this projection matrix: The vector

Pose (computer vision) (725 words) [view diff] exact match in snippet view article

camera. Usually, the camera parameters are represented in a 3 × 4 projection matrix called the camera matrix. The extrinsic parameters define the camera

Simultaneous equations model (3,353 words) [view diff] exact match in snippet view article find links to article

(}Z'_{i}PZ_{i}{\big )}^{-1}Z'_{i}Py_{i},} where P = X (X ′X)−1X ′ is the projection matrix onto the linear space spanned by the exogenous regressors X. Indirect

F4 (mathematics) (983 words) [view diff] exact match in snippet view article

of the maximal subgroups of F4 up to dimension 273 with associated projection matrix are shown below. 24-cell Albert algebra Cayley plane Dynkin diagram

Transformer (deep learning architecture) (13,111 words) [view diff] exact match in snippet view article

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}}

Orthographic projection (1,668 words) [view diff] exact match in snippet view article find links to article

{{\text{far}}+{\text{near}}}{2}}\\0&0&0&1\end{bmatrix}}} The inversion of the projection matrix P−1, which can be used as the unprojection matrix is defined: P −

ELMo (893 words) [view diff] exact match in snippet view article find links to article

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

Frobenius covariant (594 words) [view diff] exact match in snippet view article find links to article

matrix argument. If the eigenvalue λi is simple, then as an idempotent projection matrix to a one-dimensional subspace, Ai has a unit trace. The Frobenius

List of named matrices (1,336 words) [view diff] exact match in snippet view article find links to article

AA+ = A+A. Idempotent matrix or Projection Matrix A matrix that has the property A² = AA = A. The name projection matrix inspires from the observation of

Transfer-matrix method (statistical mechanics) (780 words) [view diff] exact match in snippet view article

_{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

Graphics pipeline (4,381 words) [view diff] exact match in snippet view article find links to article

distance to be visible. For reasons of efficiency, the camera and projection matrix are usually combined into a transformation matrix so that the camera

Viewing frustum (503 words) [view diff] exact match in snippet view article find links to article

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

G2 (mathematics) (2,056 words) [view diff] exact match in snippet view article

Embeddings of the maximal subgroups of G2 up to dimension 77 with associated projection matrix.

Residual sum of squares (1,055 words) [view diff] exact match in snippet view article find links to article

}]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 given by

E7 (mathematics) (2,831 words) [view diff] exact match in snippet view article

Embeddings of the maximal subgroups of E7 up to dimension 133 shown with associated projection matrix.

Optimal projection equations (3,506 words) [view diff] exact match in snippet view article find links to article

so-called optimal projection equations (OPE). The square optimal projection matrix τ ( t ) {\displaystyle \tau (t)} with dimension n {\displaystyle n}

Proof by intimidation (858 words) [view diff] no match in snippet view article find links to article

Goodman, Leo A. (1968-03-01). "An elementary approach to the population projection-matrix, to the population reproductive value, and to related topics in the

3D object recognition (1,006 words) [view diff] exact match in snippet view article find links to article

the paper detects features, and then uses RANSAC to find the affine projection matrix which best fits the unified object model to the 2D scene. If this

Moore–Penrose inverse (7,644 words) [view diff] exact match in snippet view article find links to article

(AB)^{+}A=(AB)^{+}} Finally, if ⁠ A {\displaystyle A} ⁠ is an orthogonal projection matrix, then its pseudoinverse trivially coincides with the matrix itself

Back-face culling (1,400 words) [view diff] exact match in snippet view article find links to article

the above inequality as a determinant of a matrix and applying the projection matrix to it. Another method exists based on reflection parity, which is

Grassmannian (8,402 words) [view diff] exact match in snippet view article find links to article

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}

Knowledge graph embedding (5,953 words) [view diff] exact match in snippet view article find links to article

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

Cross product (11,568 words) [view diff] exact match in snippet view article find links to article

{P} _{\mathbf {e} _{i}}^{^{\perp }}} (see below); The orthogonal projection matrix of a vector v ≠ 0 {\displaystyle \mathbf {v} \neq \mathbf {0} } is

E6 (mathematics) (3,820 words) [view diff] exact match in snippet view article

Embeddings of the maximal subgroups of E6 up to dimension 78 with associated projection matrix.

Shadow volume (2,234 words) [view diff] exact match in snippet view article find links to article

to accommodate those points, accomplished by using a specialized projection matrix. This technique reduces the accuracy of the depth buffer slightly

Trace (linear algebra) (5,564 words) [view diff] exact match in snippet view article

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 ⟹

BERT (language model) (3,528 words) [view diff] exact match in snippet view article

element-wise, then passed through a softmax layer and multiplied by a projection matrix. Absolute position encoding is included in the final self-attention

E8 (mathematics) (6,100 words) [view diff] exact match in snippet view article

Embeddings of the maximal subgroups of E8 up to dimension 248 with associated projection matrix.

Compressed sensing (5,874 words) [view diff] exact match in snippet view article find links to article

to the first-step of the iterative reconstruction process, of the projection matrix P of the fan-beam geometry, which is constrained by the data fidelity

Information bottleneck method (3,659 words) [view diff] exact match in snippet view article find links to article

T=AX\,} where matrix A {\displaystyle A\,} has orthogonal rows. The projection matrix A {\displaystyle A\,} in fact contains M {\displaystyle M\,} rows

Caravelli-Traversa-Di Ventra equation (1,978 words) [view diff] exact match in snippet view article find links to article

series to each junction. Instead, Ω {\displaystyle \Omega } is a projection matrix in which the circuit enters directly, by projecting on the fundamental

Matrix completion (6,062 words) [view diff] exact match in snippet view article find links to article

E\\&&&\operatorname {Rank} (X)\leq k.\end{aligned}}} By introducing an orthogonal projection matrix Y {\displaystyle Y} (meaning Y 2 = Y , Y = Y ′ {\displaystyle Y^{2}=Y

Spinning mirror system (1,081 words) [view diff] exact match in snippet view article find links to article

Figure 3: (a) Fiducial markers used for determining the projection matrix P. (b) The four outer mirror fiducials as seen by the projector with the mirror

Array processing (5,733 words) [view diff] no match in snippet view article find links to article

P_{\mathbf {A} }^{\perp }a(\theta ),\ where\ \mathbf {P} _{A}\ is\ a\ projection\ matrix.} 4. S e a r c h f o r a l l p o s s i b l e θ s u c h

Traceroute (film) (2,284 words) [view diff] exact match in snippet view article

individual empiricism, a narrative biographical puzzle and an experimental projection matrix. Despite continual stimulus satiation, it is wonderful fun: the film

Johnson–Lindenstrauss lemma (5,136 words) [view diff] exact match in snippet view article find links to article

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 = {

Low-rank matrix approximations (2,272 words) [view diff] exact match in snippet view article find links to article

{\textstyle {\tilde {K}}=(PX)^{T}(PX)} , where P {\textstyle P} is the projection matrix that orthogonally projects to the space spanned by the first d {\textstyle

Fine-tuning (deep learning) (1,304 words) [view diff] exact match in snippet view article

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

Xiaoming Liu (1,874 words) [view diff] exact match in snippet view article find links to article

decomposition, breaking down an image into four components: camera projection matrix, shape parameters, albedo parameters, and illumination parameters