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The vector component or vector resolute of a perpendicular to b, sometimes also called the vector rejection of a from b (denoted or a ⊥b), [1] is the orthogonal projection of a onto the plane (or, in general, hyperplane) that is orthogonal to b.
A square matrix is called a projection matrix if it is equal to its square, i.e. if =. [2]: p. 38 A square matrix is called an orthogonal projection matrix if = = for a real matrix, and respectively = = for a complex matrix, where denotes the transpose of and denotes the adjoint or Hermitian transpose of .
Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...
The orthogonal projection of the eye point onto the picture plane is called the principal vanishing point (P.P. in the scheme on the right, from the Italian term punto principale, coined during the renaissance). [7] Two relevant points of a line are: its intersection with the picture plane, and
A cylindrical vector is specified by a distance in the xy-plane, an angle, and a distance from the xy-plane (a height). The first distance, usually represented as r or ρ (the Greek letter rho), is the magnitude of the projection of the vector onto the xy-plane.
If 0° ≤ θ ≤ 90°, as in this case, the scalar projection of a on b coincides with the length of the vector projection. Vector projection of a on b (a 1), and vector rejection of a from b (a 2). In mathematics, the scalar projection of a vector on (or onto) a vector , also known as the scalar resolute of in the direction of , is given by:
The geometrical definition of a projected area is: "the rectilinear parallel projection of a surface of any shape onto a plane". This translates into the equation: A projected = ∫ A cos β d A {\displaystyle A_{\text{projected}}=\int _{A}\cos {\beta }\,dA} where A is the original area, and β {\displaystyle \beta } is the angle between ...
Projection (set theory), one of two closely related types of functions or operations in set theory; Projection (measure theory), use of a projection map in measure theory; 3D projection, any method of mapping three-dimensional points to a two-dimensional plane; Vector projection, orthogonal projection of a vector onto a straight line