Basis (Linear Algebra) - Wikipedia - en.wikipedia.org  ## Metadata - Author: **en.wikipedia.org** - Full Title: Basis (Linear Algebra) - Wikipedia - Category: #articles - Tags: #mathematic - URL: https://en.wikipedia.org/wiki/Basis_(linear_algebra) ## Highlights - In mathematics, a set B of vectors in a vector space V is called a basis if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called basis vectors. Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.[1] In other words, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.