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In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .
Vector Analysis, a textbook on vector calculus by Wilson, first published in 1901, which did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus Vector bundle , a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
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. Euclidean vectors can be added and scaled to form a vector space.
differential vector element of surface area A, with infinitesimally small magnitude and direction normal to surface S: square meter (m 2) differential element of volume V enclosed by surface S: cubic meter (m 3) electric field: newton per coulomb (N⋅C −1), or equivalently, volt per meter (V⋅m −1)
Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2 w . 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 ...
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.
Bra–ket notation or Dirac notation: if x and y are elements of an inner product space, | is the vector defined by x, and | is the covector defined by y; their inner product is . Symbols that do not belong to formulas
A vector's components change scale inversely to changes in scale to the reference axes, and consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, (with example transformations including rotation and ...