Basis vectors are fundamental vectors in a vector space that define its structure. They serve as the building blocks for all other vectors in that space. In a two-dimensional space, for example, the standard basis vectors are often represented as e₁ = (1, 0) and e₂ = (0, 1). Any vector in this space can be expressed as a combination of these basis vectors. In higher dimensions, basis vectors can be more complex but still follow the same principle. They must be linearly independent, meaning no basis vector can be formed by combining others. This property ensures that they span the entire vector space, allowing for the representation of any vector within that space.