How to calculate or simplify the determinant of the matrix formed by the coefficients of the metric tensor? Since,i am new to this chapter please keep the derivation upto the third dimension.
2026-04-09 05:47:32.1775713652
Determinant of the metric tensor
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This can be achieved through the permutations symbols:
$$ |g|=\frac{1}{3!}e^{ijk} e^{rst} g_{ir} g_{js} g_{kt}$$
Discussed in page-136 of Pavel Grinfeld's Tensor Calculus book
As pointed out by Peek-a-boo, this is indeed only true for 3-d