structural:scholar_edition, structural:summarization, information:extraction, stylistic:style_transfer
Vectors

In linear algebra, a vector space is an algebraic structure that allows for adding any two vectors and for scaling vectors. A familiar vector space is the set of all ordered pairs of real numbers; the ordered pair (a, b) is interpreted as a vector from the origin in the Euclidean plane to the point (a, b) in the plane. The sum of two vectors is obtained by adding their individual coordinates:

This addition operation is central to classical mechanics, in which velocities, accelerations and forces are all represented by vectors.