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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 ,,.
This article uses the convention that vectors are denoted in a bold font (e.g. a 1), and scalars are written in normal font (e.g. a 1). The dot product of vectors a and b is written as a ⋅ b {\displaystyle \mathbf {a} \cdot \mathbf {b} } , the norm of a is written ‖ a ‖, the angle between a and b is denoted θ .
In statistics, collinearity refers to a linear relationship between two explanatory variables. 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 to say, the north vector cannot be described in terms of the east vector, and vice versa. The third "5 miles northeast" vector is a linear combination of the other two vectors, and it makes the set of vectors linearly dependent, that is, one of the three vectors is unnecessary to define a specific location on a plane.
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.
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.
As such, for two objects and having descriptors, the similarity is defined as: = = =, where the are non-negative weights and is the similarity between the two objects regarding their -th variable. In spectral clustering , a similarity, or affinity, measure is used to transform data to overcome difficulties related to lack of convexity in the ...
As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space. Conceptually, the above integral is the equivalent of a vector dot product; two vectors are mutually independent (orthogonal) if their dot-product is zero.