Hey Max. Sure thing! We’re adding the squared L² norm, as you can see from equation 2. I’m guessing that equation 1 confused you a bit, because there the squared norm is written down explicitly as a sum over the vector’s indices.

The explanation is simple, however; The L² norm can be expressed as the square root of the inner product of the vector and itself. Thus, the squared L² norm of a vector is simply the inner product of the vector and itself, no root included!

In euclidian vector spaces the inner product is the dot product, so the dot product of a vector W[k,j] with itself is exactly the sum of its squared indices.

Is this clearer now?