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  2. Vector (mathematics and physics) - Wikipedia

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

    In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms .

  3. Vector field - Wikipedia

    en.wikipedia.org/wiki/Vector_field

    In physics, a vector is additionally distinguished by how its coordinates change when one measures the same vector with respect to a different background coordinate system. The transformation properties of vectors distinguish a vector as a geometrically distinct entity from a simple list of scalars, or from a covector .

  4. Right-hand rule - Wikipedia

    en.wikipedia.org/wiki/Right-hand_rule

    In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.

  5. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    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. Euclidean vectors can be added and scaled to form a vector space.

  6. Geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Geometric_algebra

    In mathematics, a geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors.Geometric algebra is built out of two fundamental operations, addition and the geometric product.

  7. Covariance and contravariance of vectors - Wikipedia

    en.wikipedia.org/wiki/Covariance_and_contra...

    Likewise, vectors whose components are contravariant push forward under smooth mappings, so the operation assigning the space of (contravariant) vectors to a smooth manifold is a covariant functor. Secondly, in the classical approach to differential geometry, it is not bases of the tangent bundle that are the most primitive object, but rather ...

  8. Vector calculus - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus

    Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.

  9. Screw theory - Wikipedia

    en.wikipedia.org/wiki/Screw_theory

    Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors [1] – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies. [2] [3]

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