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  2. Vector space - Wikipedia

    en.wikipedia.org/wiki/Vector_space

    When the scalar field is the real numbers, the vector space is called a real vector space, and when the scalar field is the complex numbers, the vector space is called a complex vector space. [4] These two cases are the most common ones, but vector spaces with scalars in an arbitrary field F are also commonly considered.

  3. Orbital state vectors - Wikipedia

    en.wikipedia.org/wiki/Orbital_state_vectors

    Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.

  4. Examples of vector spaces - Wikipedia

    en.wikipedia.org/wiki/Examples_of_vector_spaces

    Both vector addition and scalar multiplication are trivial. A basis for this vector space is the empty set, so that {0} is the 0-dimensional vector space over F. Every vector space over F contains a subspace isomorphic to this one. The zero vector space is conceptually different from the null space of a linear operator L, which is the kernel of L.

  5. Vector (mathematics and physics) - Wikipedia

    en.wikipedia.org/wiki/Vector_(mathematics_and...

    A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction.

  6. Position and momentum spaces - Wikipedia

    en.wikipedia.org/wiki/Position_and_momentum_spaces

    Momentum space is the set of all momentum vectors p a physical system can have; the momentum vector of a particle corresponds to its motion, with units of [mass][length][time] −1. Mathematically, the duality between position and momentum is an example of Pontryagin duality .

  7. Introduction to the mathematics of general relativity - Wikipedia

    en.wikipedia.org/wiki/Introduction_to_the...

    In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric vector [1] or spatial vector, [2] or – as here – simply a vector) is a geometric object that has both a magnitude (or length) and direction. A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "one who carries ...

  8. Tensor field - Wikipedia

    en.wikipedia.org/wiki/Tensor_field

    For example, a vector space of one dimension depending on an angle could look like a Möbius strip or alternatively like a cylinder. Given a vector bundle V over M, the corresponding field concept is called a section of the bundle: for m varying over M, a choice of vector v m in V m, where V m is the vector space "at" m.

  9. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction.