# How to compare documents in LSA?

it is mentioned in Derivation section "....You can now do the following: See how related documents j and q are in the low-dimensional space by comparing the vectors $$\Sigma_{k} d^{'}_{j}$$ and $$\Sigma_{k} d^{'}_{q}$$ (typically by cosine similarity).

My question is: as we already have the embedding vectors for both $$d^{'}_{j}$$ and $$d^{'}_{q}$$ so why do we need to multiply them by $$\Sigma_{k}$$ for comparing them, I think we can apply cosine similarity directly without multiplying by $$\Sigma_{k}$$ ?