footing, basis, ground (noun)

a relation that provides the foundation for something

"they were on a friendly footing"; "he worked on an interim basis"

basis, base, foundation, fundament, groundwork, cornerstone (noun)

the fundamental assumptions from which something is begun or developed or calculated or explained

"the whole argument rested on a basis of conjecture"

basis, base (noun)

the most important or necessary part of something

"the basis of this drink is orange juice"

basis (Noun)

A starting point, base or foundation for an argument or hypothesis.

basis (Noun)

An underlying condition or circumstance.

basis (Noun)

regular frequency

basis (Noun)

In a vector space, a linearly independent set of vectors spanning the whole vector space.

basis (Noun)

Amount paid for an investment, including commissions and other expenses.

Basis

In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system". In more general terms, a basis is a linearly independent spanning set. Given a basis of a vector space, every element of the vector space can be expressed uniquely as a finite linear combination of basis vectors, whose coefficients are referred to as vector components. Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.