(1.2 hours to learn)


A vector is is a fundamental mathematical structure that is characterized by both a direction (ordering) and a magnitude. For instance, wind has both a direction (North, South-West, etc) and a magnitude (10 km/hour) and could be represented as a vector (10 km/hour South-West). A point in Euclidean space is often represented as a vector of its coordinates and is the most common type of vector encountered. More generally, a vector is an element of a vector space -- a set that is closed under scalar multiplication and vector addition. [additional note: a vector is a very general entity that takes on many forms depending on its context, for instance, in certain vector spaces a vector could be a function such as f(x) = sin(x)]


-this concept has no prerequisites-

Core resources (read/watch one of the following)



Supplemental resources (the following are optional, but you may find them useful)


A First Course in Linear Algebra (2012)
A linear algebra textbook with proofs.
Author: Robert A. Beezer
Additional dependencies:
  • linear systems as matrices
Wolfram MathWorld
MIT Open Courseware: Linear Algebra (2011)
Videos for an introductory linear algebra course focusing on numerical methods.
Author: Gilbert Strang

See also

  • Central linear algebra concepts which build directly on vectors include: Using a small set of axioms, the basic properties of vectors can be generalized to other vector spaces ; examples include functions and polynomials.