# Difference between revisions of "Co-basis"

From Encyclopedia of Mathematics

(TeX) |
m (links) |
||

Line 1: | Line 1: | ||

{{TEX|done}} | {{TEX|done}} | ||

− | A [[ | + | A [[basis]] of a dual or [[adjoint space]]. |

====Comments==== | ====Comments==== | ||

− | A co-basis is also called a dual basis. Often the terminology "dual basis" or "co-basis" of $E^*$ is used to denote a basis $(e_i^*)$ of $E^*$ such that $e_i^*(e_j)=\delta_{ij}$ (the Kronecker delta), where $(e_i)$ is a given basis of $E$. The pair $(e_i),(e_i^*)$ is referred to as a pair of dual bases. | + | A co-basis is also called a ''dual basis''. Often the terminology "dual basis" or "co-basis" of $E^*$ is used to denote a basis $(e_i^*)$ of $E^*$ such that $e_i^*(e_j)=\delta_{ij}$ (the [[Kronecker delta]]), where $(e_i)$ is a given basis of $E$. The pair $(e_i),(e_i^*)$ is referred to as a pair of dual bases. |

## Latest revision as of 18:19, 16 October 2016

A basis of a dual or adjoint space.

#### Comments

A co-basis is also called a *dual basis*. Often the terminology "dual basis" or "co-basis" of $E^*$ is used to denote a basis $(e_i^*)$ of $E^*$ such that $e_i^*(e_j)=\delta_{ij}$ (the Kronecker delta), where $(e_i)$ is a given basis of $E$. The pair $(e_i),(e_i^*)$ is referred to as a pair of dual bases.

**How to Cite This Entry:**

Co-basis.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Co-basis&oldid=33980