# 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
• 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":

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 ... 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 - The Matrix of A Linear Transformation - Change of Basis
... Let φ1 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 ... 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 ...
Change Of Basis - Change of Coordinates of A Vector - Two Dimensions
... 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 product M-1.v ... As an example in dimension 2, a pair of vectors obtained by rotating the standard basis counterclockwise for 45 degrees ... 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 ...
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 ...
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, it refers to ... For finite extension 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 ...

### Famous quotes containing the word basis:

Brutus. How many times shall Caesar bleed in sport,
That now on Pompey’s basis lies along,
No worthier than the dust!
Cassius. So oft as that shall be,
So often shall the knot of us be called
The men that gave their country liberty.
William Shakespeare (1564–1616)

Painting dissolves the forms at its command, or tends to; it melts them into color. Drawing, on the other hand, goes about resolving forms, giving edge and essence to things. To see shapes clearly, one outlines them—whether on paper or in the mind. Therefore, Michelangelo, a profoundly cultivated man, called drawing the basis of all knowledge whatsoever.
Alexander Eliot (b. 1919)

The basis of shame is not some personal mistake of ours, but the ignominy, the humiliation we feel that we must be what we are without any choice in the matter, and that this humiliation is seen by everyone.
Milan Kundera (b. 1929)