$\sum( a^t * w )$

Question

Suppose $\vec{a}$ and $\vec{b}$ are vectors of different length.

I want to calculate

$ C = \vec{a} * \vec{b} ^T$

and then form the vector by summing over each row of C.

What is the name of this function? And does it have any useful properties

Answer 1

$C$ is the outer product between $a$ and $b$. You can sum the rows by doing $(a b^T) 1 = a (b^T 1) = (b^T 1) a$ which is $a$ times the sum of the components of $b$ where $1$ denotes the ones vector.