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  2. Kabsch algorithm - Wikipedia

    en.wikipedia.org/wiki/Kabsch_algorithm

    Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:

  3. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    A more direct method, however, is to simply calculate the trace: the sum of the diagonal elements of the rotation matrix. ... (a Lie group "translation").

  4. Transformation matrix - Wikipedia

    en.wikipedia.org/wiki/Transformation_matrix

    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 .

  5. BLEU - Wikipedia

    en.wikipedia.org/wiki/BLEU

    BLEU (bilingual evaluation understudy) is an algorithm for evaluating the quality of text which has been machine-translated from one natural language to another. Quality is considered to be the correspondence between a machine's output and that of a human: "the closer a machine translation is to a professional human translation, the better it is" – this is the central idea behind BLEU.

  6. Translation (geometry) - Wikipedia

    en.wikipedia.org/wiki/Translation_(geometry)

    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 ...

  7. Translation operator (quantum mechanics) - Wikipedia

    en.wikipedia.org/wiki/Translation_operator...

    To find the answer, translate the state by an infinitesimal amount in the -direction, calculate the rate that the state is changing, and multiply the result by . For example, if a state does not change at all when it is translated an infinitesimal amount the x {\displaystyle x} -direction, then its x {\displaystyle x} -component of momentum is 0.

  8. Word error rate - Wikipedia

    en.wikipedia.org/wiki/Word_error_rate

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  9. Translation of axes - Wikipedia

    en.wikipedia.org/wiki/Translation_of_axes

    by using a translation of axes, determine whether the locus of the equation is a parabola, ellipse, or hyperbola. Determine foci (or focus), vertices (or vertex), and eccentricity . Solution: To complete the square in x and y , write the equation in the form