Difference between revisions of "Co-basis"
From Encyclopedia of Mathematics
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A [[Basis|basis]] of a dual or [[Adjoint space|adjoint space]]. | A [[Basis|basis]] of a dual or [[Adjoint space|adjoint space]]. | ||
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| − | A co-basis is also called a dual basis. Often the terminology "dual basis" or "co-basis" of | + | 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. |
Revision as of 18:30, 21 October 2014
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
Co-basis. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Co-basis&oldid=33980