What vectorization changes

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One market per column
This array contains three firms in each of four markets. In this small example, divide every weight by its own column sum to obtain shares.

Visit columns in a Python loop
A Python loop selects one market, calls array operations, and then visits the next market. The same pattern repeats four times.

Express the update as an array
Vectorization expresses the update for every column together. The array library performs the bulk work in compiled code, with fewer trips through the Python loop.

Keep the same calculation
Both routes make twelve divisions and four column sums. They produce the same shares. Vectorization removes the loop's overhead, so the speedup is smaller when each market has more firms.

Vectorized does not mean parallel
An array expression does not promise multiple CPU cores or a GPU. Each market still has its own denominator, and an iterative solver still needs convergence checks.