What are basis vectors in a transofrm?

Basis vectors are fundamental vectors in a vector space that define its structure and orientation. In the context of a transformation, they serve as the building blocks from which other vectors can be expressed as linear combinations. When a transformation is applied, the basis vectors are mapped to new vectors, allowing for the representation of the entire vector space in a transformed coordinate system. This concept is crucial in fields like linear algebra and computer graphics, where transformations are frequently utilized.