Matrix Transpose

Transposing flips a matrix over its diagonal: row i becomes column i. An m × n matrix comes back as n × m.

Task: write transpose(matrix) that takes a list of rows and returns the transposed matrix, also as a list of rows.

• An empty matrix returns an empty list.
• Every row is guaranteed to be the same length.
• Leave the numbers exactly as they are — no rounding, no type conversion.

This shows up constantly once you start writing gradients by hand. X @ W needs X.T to get the gradient with respect to W — the shapes only line up one way, and transpose is what lines them up.