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In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context).
In mathematics, vector algebra may mean: The operations of vector addition and scalar multiplication of a vector space; The algebraic operations in vector calculus (vector analysis) – including the dot and cross products of 3-dimensional Euclidean space
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings.
It is formally defined as a directed line segment, or arrow, in a Euclidean space. [11] In pure mathematics , a vector is defined more generally as any element of a vector space . In this context, vectors are abstract entities which may or may not be characterized by a magnitude and a direction.