DefinitionA basis of a vector space, in the field of mathematics, may be described as linearly independent set of vectors that together make sure that every element in the space may be written in one and only one way as a linear combination of them. The dimension of a vector space (with algebraic basis) is a measure of the amount of vectors in the total basis for the space. Basis and dimension are two of the most basic concepts that we use to describe the structure and properties of vector spaces, and they are closely connected to the geometric and algebraic properties of vector spaces. Example : In R3, the standard basis vectors i = (1,0,0), j = (0,1,0), k = (0,0,1) are basis and dimension of R3 is 3.
