Chapter 2 operations as einsum

Three operations you already know, written with the one rule:

np.einsum('ii->', A)           # trace          == np.trace(A)
np.einsum('ij->ji', A)         # transpose      == A.T
np.einsum('ik,kj->ij', A, B)   # matrix product == A @ B

Trace repeats a letter, which selects the diagonal, and then sums it. Transpose keeps both letters but swaps their order after the arrow — nothing is summed. Matrix product shares k between two inputs and drops it.