Prove that a metric tensor is symmetric.
Assume . Because it’s irrelevant what letter we use for our indices,
So only the symmetric part of would survive the sum. As such we may as well take to be symmetric in its definition.
— edited Jun 15 ’15 at 22:48
— answered Jun 15 ’15 at 17:52
— Why is the metric tensor symmetric?
— Physics StackExchange
we cannot cancel out on both sides. In other words, we do NOT assume that in the first place.
3. “… only the symmetric part of would survive the sum” means that only the sum is physically meaningful.
— Me@2020-08-14 03:34:05 PM
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