1
$\begingroup$

How do I find a dual basis for all vectors in $R^3$ such that $v_1-3v_2+2v_3=0?$

I know the "regular" basis $B=\{ (3,1,0), (2,0,-1)\}$. But what is the dual basis?

$\endgroup$
0
$\begingroup$

Essentially the same in $R^3$. The components are the same. The dual space is a different geometric entity. Treat what you have as row vectors. The dual is the transpose of those. They will span a space of column vectors. This allows you to define an inner product between entities spanned by both.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.