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Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship. When there is perfect collinearity, the design matrix has less than full rank, and therefore the moment matrix cannot be inverted.
The collinearity equations are a set of two equations, used in photogrammetry and computer stereo vision, ... is given by a 3×3-matrix R, transforming ...
In geometry, collinearity of a set of points is the property of their lying on a single line. [1] A set of points with this property is said to be collinear (sometimes spelled as colinear [ 2 ] ). In greater generality, the term has been used for aligned objects, that is, things being "in a line" or "in a row".
Lack of perfect multicollinearity in the predictors. For standard least squares estimation methods, the design matrix X must have full column rank p ; otherwise perfect multicollinearity exists in the predictor variables, meaning a linear relationship exists between two or more predictor variables.
For a projective space defined in terms of linear algebra (as the projectivization of a vector space), a collineation is a map between the projective spaces that is order-preserving with respect to inclusion of subspaces.
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
A matrix satisfying only the first of the conditions given above, namely + =, is known as a generalized inverse. If the matrix also satisfies the second condition, namely + + = +, it is called a generalized reflexive inverse. Generalized inverses always exist but are not in general unique.
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