For the linear transformation, see Projection (linear algebra).
In statistics, the projection matrix,[1] sometimes also called the influence matrix[2] or hat matrix, maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes the influence each response value has on each fitted value.[3][4] The diagonal elements of the projection matrix are the leverages, which describe the influence each response value has on the fitted value for that same observation.
^Basilevsky, Alexander (2005). Applied Matrix Algebra in the Statistical Sciences. Dover. pp. 160–176. ISBN 0-486-44538-0.
^"Data Assimilation: Observation influence diagnostic of a data assimilation system" (PDF). Archived from the original (PDF) on 2014-09-03.
^Hoaglin, David C.; Welsch, Roy E. (February 1978). "The Hat Matrix in Regression and ANOVA" (PDF). The American Statistician. 32 (1): 17–22. doi:10.2307/2683469. hdl:1721.1/1920. JSTOR 2683469.
^David A. Freedman (2009). Statistical Models: Theory and Practice. Cambridge University Press.
In statistics, the projectionmatrix ( P ) {\displaystyle (\mathbf {P} )} , sometimes also called the influence matrix or hat matrix ( H ) {\displaystyle...
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...
In computer vision a camera matrix or (camera) projectionmatrix 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 projectionmatrix is...
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...
X(XTX)−1XT is the projectionmatrix onto the space V spanned by the columns of X. This matrix P is also sometimes called the hat matrix because it "puts...
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...
camera and projectionmatrix 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...
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...
{\displaystyle C_{n}\,} is an orthogonal projectionmatrix. That is, C n v {\displaystyle C_{n}\mathbf {v} } is a projection of v {\displaystyle \mathbf {v} \...
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...
{T} }]y=y^{\operatorname {T} }[I-H]y} , where H is the hat matrix, or the projectionmatrix in linear regression. The least-squares regression line is...
the point's true projection x {\displaystyle \mathbf {x} } . More precisely, let P {\displaystyle \mathbf {P} } be the projectionmatrix of a camera and...
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...
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...
the frustum. Together this information can be used to calculate a projectionmatrix for rendering transformation in a graphics pipeline. Kelvin Sung;...
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