A vectors is a list of things. In multivariate calculus is a list of numbers. We use them when we want to represent a coordinate in higher dimensional space, and they have three basic operations.

A vector, being a list of numbers can be visualized as an arrow in space. The vector can be visualized as an arrow whose tail is at the origin and whose tip is at the point . For this reason in multivariate calculus vectors and points are really the same thing

Vectors are denoted by a tiny arrow above their variable name, and either between parentheses as points in space or as single column matrices. Matrices are vectors extended to multiple dimensions.