Definition of "basis"

basis

noun
plural bases or (rare) baseis or (nonstandard) basises
1. A physical base or foundation.
  Quotations
  Beholding rocks from their firm basis rent;Mountain on mountain thrown,With threatening hurl, that shook th' aerial firmament!
  1695, William Congreve, To the King, on the taking of Namur, 1810, Samuel Johnson, Alexander Chalmers (biographies), The Works of the English Poets from Chaucer to Cowper, Volume 10, page 271
2. A starting point, base or foundation for an argument or hypothesis.
  Quotations
  Audio (US)(file) / I wonder if the South Korean side has any basis that its smog is from China.
  2019, VOA Learning English (public domain)
3. An underlying condition or circumstance.
  Quotations
  Hodgson may now have to bring in James Milner on the left and, on that basis, a certain amount of gloss was taken off a night on which Welbeck scored twice but barely celebrated either before leaving the pitch angrily complaining to the Slovakian referee.
  2013 September 7, Daniel Taylor, “Danny Welbeck leads England's rout of Moldova but hit by Ukraine ban”, in The Guardian‎
4. A regular frequency.
5. (agriculture, trading) The difference between the cash price a dealer pays to a farmer for his produce and an agreed reference price, which is usually the futures price at which the given crop is trading at a commodity exchange.
6. (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.
7. (accounting) Amount paid for an investment, including commissions and other expenses.
8. (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.