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  2. Four-velocity - Wikipedia

    en.wikipedia.org/wiki/Four-velocity

    If the object has mass, so that its speed is necessarily less than the speed of light, the world line may be parametrized by the proper time of the object. The four-velocity is the rate of change of four-position with respect to the proper time along the curve. The velocity, in contrast, is the rate of change of the position in (three ...

  3. Four-vector - Wikipedia

    en.wikipedia.org/wiki/Four-vector

    A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.

  4. Automatic vectorization - Wikipedia

    en.wikipedia.org/wiki/Automatic_vectorization

    Here, c[i:i+3] represents the four array elements from c[i] to c[i+3] and the vector processor can perform four operations for a single vector instruction. Since the four vector operations complete in roughly the same time as one scalar instruction, the vector approach can run up to four times faster than the original code.

  5. Proper time - Wikipedia

    en.wikipedia.org/wiki/Proper_time

    The proper time interval between two events on a world line is the change in proper time, which is independent of coordinates, and is a Lorentz scalar. [1] The interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line.

  6. Four-force - Wikipedia

    en.wikipedia.org/wiki/Four-force

    The four-force is defined as the rate of change in the four-momentum of a particle with respect to the particle's proper time.Hence,: =. For a particle of constant invariant mass >, the four-momentum is given by the relation =, where = (,) is the four-velocity.

  7. Four-gradient - Wikipedia

    en.wikipedia.org/wiki/Four-gradient

    Divergence is a vector operator that produces a signed scalar field giving the quantity of a vector field's source at each point. Note that in this metric signature [+,−,−,−] the 4-Gradient has a negative spatial component.

  8. Four-acceleration - Wikipedia

    en.wikipedia.org/wiki/Four-acceleration

    In non-inertial coordinates, which include accelerated coordinates in special relativity and all coordinates in general relativity, the acceleration four-vector is related to the four-velocity through an absolute derivative with respect to proper time.

  9. List of numerical libraries - Wikipedia

    en.wikipedia.org/wiki/List_of_numerical_libraries

    ML.NET is a free software machine learning library for the C# programming language. [3] [4] The NAG Library has C# API. Commercially licensed. NMath by CenterSpace Software: Commercial numerical component libraries for the .NET platform, including signal processing (FFT) classes, a linear algebra (LAPACK & BLAS) framework, and a statistics package.