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In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is ...
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away.
The transformation from a reference frame 1 to a reference frame 2 can be described with three translations Δx, Δy, Δz, three rotations Rx, Ry, Rz and a scale parameter μ. The Helmert transformation (named after Friedrich Robert Helmert , 1843–1917) is a geometric transformation method within a three-dimensional space .
Since translation operators all commute with each other (see above), and since each component of the momentum operator is a sum of two scaled translation operators (e.g. ^ = (^ ((,,)) ^ ((,,)))), it follows that translation operators all commute with the momentum operator, i.e. ^ ^ = ^ ^ This commutation with the momentum operator holds true ...
A rendition of the Vauquois triangle, illustrating the various approaches to the design of machine translation systems.. The direct, transfer-based machine translation and interlingual machine translation methods of machine translation all belong to RBMT but differ in the depth of analysis of the source language and the extent to which they attempt to reach a language-independent ...
The quality of a translation is inherently subjective, there is no objective or quantifiable "good." Therefore, any metric must assign quality scores so they correlate with the human judgment of quality. That is, a metric should score highly translations that humans score highly, and give low scores to those humans give low scores.
Augmented translation is a form of human translation carried out within an integrated technology environment that provides translators access to subsegment adaptive machine translation (MT) and translation memory (TM), terminology lookup (CAT), and automatic content enrichment (ACE) to aid their work, and that automates project management, file ...