Index notation
= Index notation
Index notation describes <vectors>, <matrices> and <tensors> by their components relative to a chosen <basis>. For example, <matrix multiplication> reads $(AB)_{ij}=\sum_kA_{ik}B_{kj}$. The free indices $i,j$ identify the resulting component, while $k$ is summed. An explicit summation sign avoids depending on an implicit <Einstein summation convention>.