Row-wise L2 Normalization

Normalizing a vector divides it by its own length, leaving direction intact and magnitude at exactly 1. Do it to every row of a matrix and you get a set of embeddings that can be compared purely by direction.

Task: write normalize_rows(matrix) returning the matrix with each row scaled to unit length, rounded to 4 decimal places.

• Rows are normalized independently — nothing is shared between them.
• A row of all zeros has no direction and no length to divide by; return it unchanged as zeros.
• An empty matrix returns an empty list.

This is what makes cosine similarity cheap. Once every row is unit length, the cosine between two of them is just their dot product — no division left to do, which is exactly how vector databases compare millions of embeddings quickly.