basis (Noun) — A relation that provides the foundation for something. ex. "he worked on an interim basis"
basis (Noun) — The fundamental assumptions from which something is begun, developed, calculated or explained. ex. "the whole argument rested on a basis of conjecture"
basis (Noun) — The most important or necessary part of something. ex. "the basis of this drink is orange juice"
basis (Noun) — (mathematics) in a vector space, a linearly independent set of vectors spanning the whole vector space.