Converting Summation into matrix form

Question

Would require some help on this

$\sum{r_i^2 * e_i^2}$

would it be equivalent to

$(re)^T(re)$. It does seem to be equivalent but i cannot seem to prove it.

Assuming r and e are both vectors.

Thanks!

Answer 1

Just write it out componentwise for two dimensional vectors.

If $re$ is the dot product as you say in the comments it is not. $\sum r_i^2*e_i^2=r_1^2e_1^2+r_2^2e_2^2$ while $re$ is a scalar $(re)=r_1e_1+r_2e_2$ and $(re)^T(re)$ is the square of this which includes a term $2r_1e_1r_2e_2$

If $(re)$ is a vector that is the componentwise product of $r$ and $e$ it is true. Write it out for yourself.