Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can't we construct a mapping from $V^3(R^1)$ to $R$ such that $a.b.c = a_{x}b_{x}c_{x}+a_{y}b_{y}c_{y}+a_{z}b_{z}c_{z}$ (a,b,c are vectors in $V^3(R^1)$ ) and more generally $a^n$ , $a.b.c.d.e...$ mappings so that $(a^p)^{1/p}$ is the $p$ norm of vectors in $V^3$ ?

share|improve this question
    
It would be nice to have a nice way to write products like these. Similarly to $a^Tb$ for `dual' inner products. –  Thomas Ahle Mar 3 at 21:28

1 Answer 1

I found the solution. To 'dot' together vectors $a$, $b$, $c$, make the diagonal matrix $B$ and write:

$a^T B c$

If you have more than three vectors to 'dot', just add more diagonal matrices in the middle.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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