Basis (mathematics): Difference between revisions
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* In an [[exponent|exponential expression]], the [[exponent|base]] is the quantity upon which the exponent is placed as a superscript. | * In an [[exponent|exponential expression]], the [[exponent|base]] is the quantity upon which the exponent is placed as a superscript. | ||
* In [[logarithm]]s, the base is the quantity raised to the power of the logarithm to return the given number. | * In [[logarithm]]s, the base is the quantity raised to the power of the logarithm to return the given number. | ||
* A [[basis (linear algebra)|basis]] is a [[linearly independent]] [[spanning set]] in [[linear algebra]]. | * A [[basis (linear algebra)|basis]] is a [[Linear independence|linearly independent]] [[spanning set]] in [[linear algebra]]. | ||
* A [[basis (topology)|basis]] (or base) for a [[topology]] is a system of [[open set]]s that generate the topology. | * A [[basis (topology)|basis]] (or base) for a [[topology]] is a system of [[open set]]s that generate the topology. | ||
* A [[filter base]] is a collection of sets that generates a [[filter]]. | * A [[filter base]] is a collection of sets that generates a [[filter]]. | ||
* In [[algebraic geometry]], there exists the notion of a [[Gröbner basis]] of an [[ideal]]. | * In [[algebraic geometry]], there exists the notion of a [[Gröbner basis]] of an [[ideal]]. | ||
* A [[uniform base]] is a family of relations on a set that generates a [[uniform space]] structure. | * A [[uniform base]] is a family of relations on a set that generates a [[uniform space]] structure. | ||
Revision as of 16:44, 6 January 2009
This is a disambiguation page for the different uses of the words base or basis in mathematics.
- In an exponential expression, the base is the quantity upon which the exponent is placed as a superscript.
- In logarithms, the base is the quantity raised to the power of the logarithm to return the given number.
- A basis is a linearly independent spanning set in linear algebra.
- A basis (or base) for a topology is a system of open sets that generate the topology.
- A filter base is a collection of sets that generates a filter.
- In algebraic geometry, there exists the notion of a Gröbner basis of an ideal.
- A uniform base is a family of relations on a set that generates a uniform space structure.