# vectors

(1.2 hours to learn)

## Summary

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)]

## Context

-this concept has no prerequisites-

## Core resources (read/watch one of the following)

## -Free-

→ Khan Academy: Linear Algebra

## -Paid-

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 1.1, "Vectors in R^n", pages 1-6

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 1.1, pages 2-6

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

## -Free-

→ A First Course in Linear Algebra (2012)

A linear algebra textbook with proofs.

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.

## 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.