Bases of dual spaces I am given that dual to the basis $B=\{v_1,v_2,...,v_n\}$ of the vector space $V$ is the dual basis $\{f_1,f_2,...,f_n\}$ of $V^*$ where $V^*$ is the dual space of $V$. 

How do I find the dual basis with respect to another basis, $B&#39;$ of $V$? 

I know that any basis of $V$ are composed of  vectors which are linear combinations of $\{v_1,v_2,...,v_n\}$. And then...? 

Thanks.
How do you know $\{f_{1},...,f_{n}\}$ ? If you know the relation between $\{v_{1},...,v_{n}\}$ and $\{f_{1},...,f_{n}\}$ then you can find the dual basis with respect to another basis. 

I do not think this kind of question appropriate for MathstackExchange. Next time, you should try to find the answer for this kind of question at wikipedia first :
http://en.wikipedia.org/wiki/Dual_basis
How do you know $\{f_{1},...,f_{n}\}$ ? If you know the relation between $\{v_{1},...,v_{n}\}$ and $\{f_{1},...,f_{n}\}$ then you can find the dual basis with respect to another basis. 

I do not think this kind of question appropriate for MathstackExchange. Next time, you should try to find the answer for this kind of question at wikipedia first :
http://en.wikipedia.org/wiki/Dual_basis