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 three-dimensional space, for example, the standard basis vectors are often represented as i, j, and k, corresponding to the x, y, and z axes, respectively. Any vector in this space can be expressed as a combination of these basis vectors. Each basis vector is linearly independent, meaning no basis vector can be formed by combining others. This independence ensures that the basis vectors span the entire vector space, allowing for unique representation of vectors. In mathematical terms, if you have a vector v, it can be written as a linear combination of the basis vectors: v = ai + bj + ck, where a, b, and c are scalars.