basis
Pluralbases
- 1The facts, ideas or conditions on which something is based or from which it develops.
The lawyer built her entire case on the basis of a single witness.
Several recent studies provide the basis for these recommendations.
UsageOften on the basis of something or the basis for it: the basis for a decision. The plural is bases.
- 2How often something happens or is done, such as daily, weekly or irregularly; usually in the phrase on a … basis.
The team meets on a regular basis to review its progress.
Volunteers are rotated through the shelter on a monthly basis.
UsageUsually on a daily, weekly or regular basis. A single word (daily, regularly) often says the same more simply.
- 3The terms or arrangement on which something is done or organized, such as part-time, temporary or unpaid work; usually in the phrase on a … basis.
Most of the museum's guides serve on a voluntary basis.
Tickets will be given out on a first-come, first-served basis.
UsageUsually on a voluntary, part-time or trial basis; the word before basis carries the meaning.
Similarfooting
- 4A physical base or foundation on which a structure rests.
We see here the ground-plan of masses of houses, with their upper walls of fire-baked brick on a basis of stone.
1907, Ronald M. Burrows, The Discoveries In CreteSimilarbase, foundation, pedestal
Note
Ronald M. Burrows could still write in 1907 of fire-baked brick walls "on a basis of stone."
Less common meanings
- 5In finance and tax, the total cost of acquiring an investment, counting commissions and other expenses as well as the price.
The investor's basis in the property included the purchase price and closing costs.
Capital gains are found by subtracting the basis from the final sale price.
UsageUsually your basis in an investment, such as a house or stock; cost basis and adjusted basis are common terms.
Note
An accountant's figure and the starting point for tax on a sale: subtract the adjusted basis from the amount realized, the proceeds after selling costs, and what remains is the capital gain or loss. Commissions and other purchase expenses are folded in, so the basis can be higher than the bare purchase price. It is the investor's own number, unlike the grain trader's basis, which measures a gap between two market prices.
Checked 5 Nov 2026 · 5 facts
- Basis is used to calculate gain or loss for tax purposes. irs.gov
- Use adjusted basis and the amount realized after selling expenses, rather than simply acquisition cost and gross sale price. irs.gov
- Purchase commissions and other acquisition costs are included in basis. irs.gov
- Investment basis is specific to the investor's acquisition and subsequent adjustments. en.wikipedia.org
- The grain trader's basis measures a difference between market prices. alberta.ca
- 6In a vector space, a set of linearly independent vectors that together span the entire space.
Like primary colors that can be mixed to produce any other color.
Any vector in the plane can be written using a basis of two independent vectors.
Changing the basis can greatly simplify the equations describing a transformation.
Note
Linear algebra's way of giving a space coordinates. Because the vectors are independent and together reach everything, each vector in the space is written as exactly one combination of them, and the number needed equals the dimension of the space. The plural is bases: a space usually has many bases, which is why changing basis is possible. Do not confuse it with the covering family of subsets, which collects sets rather than vectors.
Checked 5 Nov 2026 · 6 facts
- A basis gives vectors coordinates through unique linear combinations. mathbooks.unl.edu
- The number of vectors in a basis equals the dimension. cs.yale.edu
- The plural of basis is bases. en.wikipedia.org
- A space can have many bases, but this is not universal: the zero vector space has only the empty basis. shoup.net
- Changing basis changes the coordinates used to represent vectors. interactivetextbooks.tudelft.nl
- A topological basis consists of subsets rather than vectors. stacks.math.columbia.edu
- 7In commodity trading, the difference between the local cash price paid for a crop and the reference price, usually the futures price for that crop on an exchange.
- 8In topology, a collection of subsets of a set that covers the set and, for any two members sharing a point, contains a third member inside their overlap that also holds that point.
Practice
Can you tell the meanings of basis apart? Answer 3 quick questions from this page, or write your own sentence and AI will check it.
Origin
The root is Proto-Indo-European *gʷem- (which also gives 'come'); from it was derived *gʷémtis, which became Ancient Greek βάσις (básis) and then Latin basis, the source of the English word. It is a doublet of base.