**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
- Radial basis function
- 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":

**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 ...

**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 ...

**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 ...

**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 ...

**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)