A Quick and Simple Dictionary

basis

1. Noun.  A starting point, base or foundation for an argument or hypothesis.
2. Noun.  An underlying condition or circumstance.
3. Noun.  regular frequency.
4. Noun.  (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.
5. Noun.  (accounting) Amount paid for an investment, including commissions and other expenses.
6. Noun.  (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.