Vectors

Synonyms

Directed quantities; Elements of linear spaces; Members of vector spaces; Vectors in finite dimensional spaces

Definitions

A vector is a tensor of order one. Intuitively, it is a quantity having magnitude and direction (and possibly a physical unit). The vector concept is typically introduced in basic mathematics, where a vector is characterized as a directed line segment.

Although vectors can be defined and studied in ${\mathbb {R}}^n$, the present article focuses on the case n = 3.

Vectors of Linear Algebra and of Mechanics

The term vectorhas a wide spectrum of meaning, ranging from an arrow drawn in the coordinate plane to a “vector of success” that is difficult to identify with an arrow. In linear algebra, the term is a synonym for a member or element of a linear (or vector) space, a set of elements that can be added and multiplied by scalars in such a way that the results fall within the same space and, moreover, such that the usual linear space axioms apply. The...