Difference between revisions of "Co-basis"
From Encyclopedia of Mathematics
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| − | 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=39419
Co-basis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Co-basis&oldid=39419