Links: [[Math]] [[Linear Algebra]] Type: #to-tidy Related: [[Tensor]] --- *Note: Interestingly vectors and vector spaces are defined in a somewhat mutually recursive fashion* - Vectors have a number *n* of components - e.g. a vector v with 2 components from **N** is really just N^2 (i.e. N x N the tuple of 2 scalars from N) - A vector space **V** - A set of elements (called vectors) that is closed under - vector addition - scalar multiplication In general, the scalars are from a field ***F*** - We call *V* a vector space over *F* - All elements of a vector space must be vectors of the same number of components over the same field