ABSTRACT

For an expression written in terms of a high rank tensor or the multiplication of several vectors or tensors, if two indices are repeated, the summation convention will be applied in the range of (1, 2, 3). For example,

aibi = 3∑

i=1 aibi = a1b1 + a2b2 + a3b3 (2.1)

The above expression becomes one scalar. The repeated index is also called dummy index because it can be replaced by other symbols without changing the outcome. For example, aibi = ajbj = akbk where the repeated indices i, j, and k are dummy indices.