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  2. Vector projection - Wikipedia

    en.wikipedia.org/wiki/Vector_projection

    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 .

  3. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    A basic 3D rotation (also called elemental rotation) is a rotation about one of the axes of a coordinate system. The following three basic rotation matrices rotate vectors by an angle θ about the x-, y-, or z-axis, in three dimensions, using the right-hand rule—which codifies their alternating signs.

  4. 3D projection - Wikipedia

    en.wikipedia.org/wiki/3D_projection

    These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. 3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual ...

  5. Transformer (deep learning architecture) - Wikipedia

    en.wikipedia.org/wiki/Transformer_(deep_learning...

    For many years, sequence modelling and generation was done by using plain recurrent neural networks (RNNs). A well-cited early example was the Elman network (1990). In theory, the information from one token can propagate arbitrarily far down the sequence, but in practice the vanishing-gradient problem leaves the model's state at the end of a long sentence without precise, extractable ...

  6. UV mapping - Wikipedia

    en.wikipedia.org/wiki/UV_mapping

    UV mapping is the 3D modeling process of projecting a 3D model's surface to a 2D image for texture mapping. The letters "U" and "V" denote the axes of the 2D texture because "X", "Y", and "Z" are already used to denote the axes of the 3D object in model space, while "W" (in addition to XYZ) is used in calculating quaternion rotations, a common ...

  7. Gram–Schmidt process - Wikipedia

    en.wikipedia.org/wiki/Gram–Schmidt_process

    The vector projection of a vector on a nonzero vector is defined as [note 1] ⁡ = , , , where , denotes the inner product of the vectors and . This means that proj u ⁡ ( v ) {\displaystyle \operatorname {proj} _{\mathbf {u} }(\mathbf {v} )} is the orthogonal projection of v {\displaystyle \mathbf {v} } onto the line spanned by u ...

  8. Projection (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Projection_(linear_algebra)

    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 .

  9. Direct-quadrature-zero transformation - Wikipedia

    en.wikipedia.org/wiki/Direct-quadrature-zero...

    Plane of the vectors without common mode indicated by the hexagonal outline. The Z axis is orthogonal to this plane, and the X axis is parallel to the projection of the A axis onto the zero plane. The X and Y basis vectors are on the zero plane. Notice that the X axis is parallel to the projection of the A axis onto the zero plane.

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