Einstein Summation
Tensors only supports single and pairwise tensors summations.
Primitive operations
Index summation
\[U = \sum_i V_i\]
Index transposition
\[U_{ji} = V_{ij}\]
Diagonal
\[U_i = V_{ii}\]
Hadamard or element-wise product
\[C_i = A \boxtimes B = A_i B_i\]
Outer or tensor product
\[C_{ij} = A \otimes B = A_i B_j\]
Composite operations
Trace
\[U = \sum_i V_{ii}\]
Inner or scalar product
\[C = A \cdot B = \sum_i A_i B_i\]
Matrix multiplication
\[C_{ij} = \sum_k A_{ik} B_{kj}\]