section_path: In calculus/Vector-valued function
section_name: Vector-valued function
paragraph_text: Vector-valued function
  
  When the elements of the codomain of a function are vectors, the function is said to be a vector-valued function. These functions are particularly useful in applications, for example modeling physical properties. For example, the function that associates to each point of a fluid its velocity vector is a vector-valued function.
  
  Some vector-valued functions are defined on a subset of R n {\displaystyle \mathbb {R} ^{n}} or other spaces that share geometric or topological properties of R n {\displaystyle \mathbb {R} ^{n}}, such as manifolds. These vector-valued functions are given the name vector fields.