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Two variables are perfectly collinear if there is an exact linear relationship between the two, so the correlation between them is equal to 1 or −1. That is, X 1 and X 2 are perfectly collinear if there exist parameters λ 0 {\displaystyle \lambda _{0}} and λ 1 {\displaystyle \lambda _{1}} such that, for all observations i , we have
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.
In statistics, multicollinearity or collinearity is a situation where the predictors in a regression model are linearly dependent. Perfect multicollinearity refers to a situation where the predictive variables have an exact linear relationship.
Let x, y, and z refer to a coordinate system with the x- and y-axis in the sensor plane. Denote the coordinates of the point P on the object by ,,, the coordinates of the image point of P on the sensor plane by x and y and the coordinates of the projection (optical) centre by ,,.
While the projective linear group of the projective line is 3-transitive (any three distinct points can be mapped to any other three points), and indeed simply 3-transitive (there is a unique projective map taking any triple to another triple), with the cross ratio thus being the unique projective invariant of a set of four points, there are ...
Simply, a collineation is a one-to-one map from one projective space to another, or from a projective space to itself, such that the images of collinear points are themselves collinear. One may formalize this using various ways of presenting a projective space. Also, the case of the projective line is special, and hence generally treated ...
The TRIAD method is the earliest published algorithm for determining spacecraft attitude, which was first introduced by Harold Black in 1964. [1] [2] [3] Given the knowledge of two vectors in the reference and body coordinates of a satellite, the TRIAD algorithm obtains the direction cosine matrix relating to both frames.