Metric tensor: trace

Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – Chapter 6;  5.

A specific case of the trace of a tensor is the trace of the metric tensor, which is given by {g_{ij}g^{ij}}. Since {g^{ij}} is the inverse of the metric tensor {g_{ij}}, {g_{ik}g^{kj}=\delta_{\;\; i}^{j}} is the identity matrix, which means it is diagonal with every diagonal element equal to 1. The trace of the identity matrix is simply {n}, the dimension of the matrix. Thus in 2-d it would be {n=2} and so on.

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