Noun

basis (plural bases or (rare) baseis)

1. A starting point, base or foundation for an argument or hypothesis.
2. An underlying condition or circumstance.
3. (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.
4. (accounting) Amount paid for an investment, including commissions and other expenses.
5. (topology) A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.

   The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.

Derived terms

• basis point (4)
• tax basis
• cost basis
• basic

Synonyms

• (starting point for discussion): base

Basis

Basis may refer to

• Cost basis, in income tax law, the original cost of property adjusted for factors such as depreciation.
• Basis future, the value differential between a future and the spot price
• Basis (options), the value differential between a call option and a put option
• Cost basis, in the calculation of capital gains
• Basis (crystal structure), positions of the atoms inside the unit cell
• BASIS International, a software company
• in Renaissance music, the bassline was sometimes called the basis
• BASIS Schools, a group of high-expectations schools in Arizona, USA.

In mathematics:

• Basis (linear algebra)
  • Schauder basis
• Basis (topology)
• Basis (universal algebra)
• Gröbner basis
• Greedoid
• Generating set of a group

In chemistry:

• Basis set (chemistry)

In people:

• Dimitris Basis Greek singer