basis

1. (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.Examples: "Included in the basis could be elevation, cleaning, freight by truck and/or rail, government inspection fees, administration fees, interest and storage charges as well as allowance for risk and profit for the grain dealer."

2. (linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.

3. (accounting) Amount paid for an investment, including commissions and other expenses.

4. (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.Examples: "The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis."