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These properties are essential for comprehension the actions from the tensor in numerous coordinate methods.
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First off english is just not my mom tongue sorry. I wish to ask If you're able to aid me with a number of the properties of your levi-civita symbol.
In summary, the conversation is regarding the Qualities from the Levi-Civita image. The 1st part discusses a method that doesn't appear to match the expected reply, and the next portion will involve proving An additional formulation. The dialogue finishes that has a last Alternative that satisfies the properties.
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The covariant Levi-Civita tensor (also called the Riemannian quantity variety) in any coordinate method that matches the chosen orientation is
The true secret defining assets with the symbol is overall antisymmetry while in the indices. When any two indices are interchanged, equal or not, the symbol is negated:
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