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ε i j k ε l m n =
ε i j ε i n = δ j n displaystyle varepsilon _ ij varepsilon ^ in = delta _ j ^ n
These Attributes are important for understanding the behavior from the tensor in numerous coordinate methods.
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The subsequent are examples of the final identification over specialised to Minkowski Room (Using the destructive signal arising from the odd amount of negatives inside the signature of your metric tensor in both signal convention):
In Einstein notation, the duplication in the i index implies the sum on i. The earlier is then denoted εijkεimn = δjmδkn − δjnδkm.
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E α β γ δ = g α ζ g β η g γ θ g δ ι E ζ η θ ι . displaystyle E^ alpha beta gamma delta =g^ alpha zeta g^ beta eta g^ gamma theta g^ delta iota E_ zeta eta theta iota ,.
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