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Hamilton derived the word vector from the Latin vehere, to carry. [7] Hamilton conceived a vector as the "difference of its two extreme points." [6] For Hamilton, a vector was always a three-dimensional entity, having three co-ordinates relative to any given co-ordinate system, including but not limited to both polar and rectangular systems. [8]
For two elements a 1 + b 1 i + c 1 j + d 1 k and a 2 + b 2 i + c 2 j + d 2 k, their product, called the Hamilton product (a 1 + b 1 i + c 1 j + d 1 k) (a 2 + b 2 i + c 2 j + d 2 k), is determined by the products of the basis elements and the distributive law. The distributive law makes it possible to expand the product so that it is a sum of ...
In mathematics, quaternions are a non-commutative number system that extends the complex numbers.Quaternions and their applications to rotations were first described in print by Olinde Rodrigues in all but name in 1840, [1] but independently discovered by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space.
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
In mathematics, a quaternion algebra over a field F is a central simple algebra A over F [1] [2] that has dimension 4 over F.Every quaternion algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension), i.e. for a suitable field extension K of F, is isomorphic to the 2 × 2 matrix algebra over K.
The story itself is considered a performance so there is a synergy among the aforementioned elements. [1] In the story, the narrator may draw attention to the narrative or to himself as storyteller. [2] The structure often includes the following: Tell riddles to test the audience. Audience becomes a chorus and comments on the story.