A transposed NumPy array presents matrix axes in a different order without necessarily copying the data. The resulting view shares memory with the original; its strides describe how many bytes to move along each axis to find the next element. section 4.1.2
Because transposition is a fast view operation, it can also help align dimensions for broadcasting. For example, transpose a matrix, add a vector whose length matches the original row count, then transpose the result back to apply the vector row by row. section 4.2.2
m2x5 = linear.reshape((2, 5))
print(np.shares_memory(linear, m2x5))
print("2x5", m2x5.shape)
print("2x5 corners", m2x5[0, 0], m2x5[0, 4],
m2x5[2, 0], m2x5[2, 4])
m5x2 = m2x5.T
print(np.shares_memory(m2x5, m5x2))
print("5x2", m5x2.shape)
print("5x2 corners", m5x2[0, 0], m5x2[0, 1],
m5x2[4, 0], m5x2[4, 1])
Inspect how reshaping and `.T` change array shapes while `np.shares_memory` checks whether the arrays share storage. section 4.1.2
Shape can affect runtime
A reported Game of Life benchmark took 44 seconds for a 400 × 900,000 map over four generations, versus 20 seconds for its transposed 900,000 × 400 shape on the same computer. The cause is deferred, and results may differ across computers. section 5.6.2
