Pairwise Cosine Similarity Matrix

Difficulty: Medium · Concept: Word Embeddings — The Distributional Hypothesis

Cosine Similarity From Scratch compared exactly two vectors. A real embedding search or clustering step needs every pair at once: given $n$ vectors, produce the full $n \times n$ matrix where entry $(i, j)$ is the cosine similarity between vector $i$ and vector $j$ — exactly the computation underneath comparing a batch of query embeddings against a batch of candidates, or building the similarity graph a vector database index is organized around.

The genuine edge case: a vector with zero magnitude (all-zero) makes cosine similarity undefined for every pair it's involved in — $\frac{\cdot}{0}$ has no answer, so the whole computation has to fail loudly rather than silently produce a nan-filled row.

Your task: implement cosine_similarity_matrix(vectors), returning a list of lists (the matrix). Raise ValueError if any vector has zero magnitude.

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