A basis vector is a fundamental concept in linear algebra that represents a direction in a vector space. In a given space, a set of basis vectors can be combined through linear combinations to form any vector within that space. For example, in a two-dimensional space, the standard basis vectors are often represented as e₁ = (1, 0) and e₂ = (0, 1), which correspond to the x and y axes. Each basis vector is independent, meaning no basis vector can be expressed as a combination of the others. This independence is crucial for defining the dimensionality of the space. For instance, in a three-dimensional space, three basis vectors are needed, such as e₁, e₂, and e₃, to represent any point in that space accurately.