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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. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
"A science fiction story is a story built around human beings, with a human problem, and a human solution, which would not have happened at all without its scientific content." [13] Basil Davenport. 1955. "Science fiction is fiction based upon some imagined development of science, or upon the extrapolation of a tendency in society." [14] Edmund ...
The term vector was coined by W. R. Hamilton around 1843, as he revealed quaternions, a system which uses vectors and scalars to span a four-dimensional space. For a quaternion q = a + b i + c j + d k, Hamilton used two projections: S q = a , for the scalar part of q , and V q = b i + c j + d k, the vector part.
A vector may also result from the evaluation, at a particular instant, of a continuous vector-valued function (e.g., the pendulum equation). In the natural sciences, the term "vector quantity" also encompasses vector fields defined over a two-or three-dimensional region of space, such as wind velocity over Earth's surface.
Projection (mathematics), any of several different types of geometrical mappings Projection (linear algebra), a linear transformation P from a vector space to itself such that P 2 = P; 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 ...
Holography served as an inspiration for many video games with the science fiction elements. In many titles, fictional holographic technology has been used to reflect real life misrepresentations of potential military use of holograms, such as the "mirage tanks" in Command & Conquer: Red Alert 2 that can disguise themselves as trees. [2]
A matrix, has its column space depicted as the green line. The projection of some vector onto the column space of is the vector . From the figure, it is clear that the closest point from the vector onto the column space of , is , and is one where we can draw a line orthogonal to the column space of .
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: