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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 .
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
Symbol Meaning SI unit of measure magnetic vector potential: tesla meter (T⋅m) : area: square meter (m 2) : amplitude: meter: atomic mass number: unitless acceleration: meter per second squared (m/s 2)
In introductory physics textbooks, the standard basis vectors are often denoted ,, instead (or ^, ^, ^, in which the hat symbol ^ typically denotes unit vectors). In this case, the scalar and vector components are denoted respectively a x , a y , a z , and a x , a y , a z (note the difference in boldface).
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.
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 .
Such vectors are typically denoted with over arrows (), boldface or indices (). In quantum mechanics, a quantum state is typically represented as an element of a complex Hilbert space , for example, the infinite-dimensional vector space of all possible wavefunctions (square integrable functions mapping each point of 3D space to a complex number ...
Similarly, a bivector in three dimensions has an attitude given by the family of planes associated with it (possibly specified by the normal line common to these planes [6]), an orientation (sometimes denoted by a curved arrow in the plane) indicating a choice of sense of traversal of its boundary (its circulation), and a magnitude given by the ...