Compute Pointwise Multiplication by hand

Question

How could we compute the pointwise multiplication of two vectors? In example:

A = [1 2 3]'

What is the pointwise multiplication of A.^2? (like computational programs using)

In short: what steps should be take to convert: A = [1 2 3]' to A^2 = [1 4 9]'

Answer 1

$A = \{a_1, a_2, a_3\}$

$A\cdot A= A^2 = \{a_1\cdot a_1, a_2\cdot a_2, a_3\cdot a_3\}$

In your example:

$A.A = A^2 = \{1^2,2^2,3^2\} = \{1,4,9\}$