Vector multiplication of squared vectors

Question

I would like to have a mathematical expression for this problem:

A = [n x 1] (i.e. 1;2;3) B = [n x 1] (i.e. 4;5;6)

I'm looking for the dot multiplication of both vectors pointwise-squared.

c = A^2*B^2

The answer should be a scalar with a value of 440 The matlab expression looks like:

c = ([1;2;3].^2)'*([4;5;6].^2) = 440

Answer 1

Let $\circ$ denote the hadamard product.

$$\sum_{i=1}^nA_i^2B_i^2=\sum_{i=1}^n(A_iB_i)^2=\sum_{i=1}^n (A \circ B)_i^2=\left\|A \circ B\right\|_2^2$$