# Basis

Basis may refer to

• 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 economics:

• Adjusted basis, the net cost of an asset after adjusting for various tax-related items
• Basis of futures, the value differential between a future and the spot price
• Basis (options), the value differential between a call option and a put option
• Basis point, 0.01%, often used in the context of interest rates
• Basis trading, a trading strategy consisting of the purchase of a security and the sale of a similar security
• Cost basis, in income tax law, the original cost of property adjusted for factors such as depreciation
• Tax basis, cost of an asset

In mathematics:

• Basis function
• Basis (linear algebra)
• Dual basis
• Orthonormal basis
• Schauder basis
• Basis (universal algebra)
• Generating set of an ideal (ring theory):
• Gröbner basis
• Hilbert's basis theorem
• Generating set of a group
• Base (topology) of a topology: a generating set of the open sets of the topology
• Change of basis
• Greedoid
• Normal basis
• Polynomial basis
• Standard basis
• Transcendence basis of a field extension

In chemistry and physics:

• Basis (crystal structure), the positions of the atoms inside the unit cell
• Basis set (chemistry)
• Dry basis, an expression of a calculation in which the presence of water is ignored

People:

• Dimitris Basis, Greek singer
• Liron Basis, Israeli footballer

### Other articles related to "basis":

Change Of Basis - Change of Coordinates of A Vector - Three Dimensions
... For example, be a new basis given by its Euler angles ... The matrix of the basis will have as columns the components of each vector ... Again, any vector of the space can be changed to this new basis by left-multiplying its components by the inverse of this matrix ...
Change Of Basis - Change of Coordinates of A Vector - Two Dimensions
... a matrix M whose columns are the vectors of the new basis of the space (new basis matrix), the new coordinates for a column vector v are given by the matrix. 2, a pair of vectors obtained by rotating the standard basis counterclockwise for 45 degrees ... the coordinates of these vectors is If we want to change any vector of the space to this new basis, we only need to left-multiply its components by the inverse of this matrix ...
Canonical Basis
... In mathematics, a canonical basis is a basis of an algebraic structure that is canonical in a sense that depends on the precise context In a coordinate space, and more generally in a free module ... fields, it means the polynomial basis ... In representation theory, Lusztig's canonical basis and closely related Kashiwara's crystal basis in quantum groups and their representations ...
Change Of Basis - The Matrix of A Linear Transformation - Change of Basis
1 and φ2 be the coordinate isomorphisms taking the usual basis in Rn to the first and second bases for V, and let ψ1 and ψ2 be the isomorphisms taking the usual basis in Rm to the first and second bases ... Given that the change of basis has once the basis matrix and once its inverse, this objects are said to be 1-co, 1-contra-variants ...
Rational Basis Review - Applicability
... In modern constitutional law, the rational basis test is applied to constitutional challenges of both federal law and state law (via the Fourteenth Amendment) ... A law, when challenged, must have a rational basis without which it might violate right of a person under the U.S ... To understand the concept of rational basis review, it is easier to understand what it is not ...

### Famous quotes containing the word basis:

Compassion has no place in the natural order of the world which operates on the basis of necessity. Compassion opposes this order and is therefore best thought of as being in some way supernatural.
John Berger (b. 1926)

The self ... might be regarded as a sort of citadel of the mind, fortified without and containing selected treasures within, while love is an undivided share in the rest of the universe. In a healthy mind each contributes to the growth of the other: what we love intensely or for a long time we are likely to bring within the citadel, and to assert as part of ourself. On the other hand, it is only on the basis of a substantial self that a person is capable of progressive sympathy or love.
Charles Horton Cooley (1864–1929)

Self-alienation is the source of all degradation as well as, on the contrary, the basis of all true elevation. The first step will be a look inward, an isolating contemplation of our self. Whoever remains standing here proceeds only halfway. The second step must be an active look outward, an autonomous, determined observation of the outer world.
Novalis [Friedrich Von Hardenberg] (1772–1801)