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The 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 a onto a straight line parallel to b.
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).
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 .
In algebraic geometry, Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces objects with the typical properties of projective spaces and projective varieties. The construction, while not functorial, is a fundamental tool in scheme theory.
Meridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 aspect. 1949 McBryde–Thomas flat-pole quartic = McBryde–Thomas #4: Pseudocylindrical Equal-area Felix W. McBryde, Paul Thomas Standard parallels at 33°45′N/S; parallels are unequal in spacing and scale; meridians are fourth-order ...
Once again, if Δφ may be read directly from an accurate latitude scale on the map, then the rhumb distance between map points with latitudes φ 1 and φ 2 is given by the above. If there is no such scale then the ruler distances between the end points and the equator, y 1 and y 2, give the result via an inverse formula:
The commutativity of this diagram is the universality of the projection π, for any map f and set X.. Generally, a mapping where the domain and codomain are the same set (or mathematical structure) is a projection if the mapping is idempotent, which means that a projection is equal to its composition with itself.
The Proj construction in fact gives more than a mere scheme: a sheaf in graded modules over the structure sheaf is defined in the process. The homogeneous components of this graded sheaf are denoted (), the Serre twisting sheaves. All of these sheaves are in fact line bundles.