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or Minkowski Room. The values from the Levi-Civita image are independent of any metric tensor and coordinate method. Also, the precise term "symbol" emphasizes that it is not a tensor thanks to how it transforms amongst coordinate programs; nevertheless it can be interpreted as being a tensor density.

These Houses are important for comprehending the habits on the tensor in different coordinate techniques.

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then still left side is zero, and proper aspect is likewise zero given that two of its rows are equivalent. Likewise for j c = j c + 1 displaystyle j_ c =j_ c+one

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Utilizing the capital pi notation Π for standard multiplication of quantities, an express expression for the image is:[citation required]

but see that if the metric signature contains an odd quantity of detrimental eigenvalues q, then the indication with the parts of the tensor vary within the standard Levi-Civita image:

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E α β γ δ E ρ σ μ ν = − g α ζ g β η g γ θ g δ ι δ ρ σ μ ν ζ η θ ι E α β γ δ E ρ σ μ ν = − g α ζ g β η g γ θ g δ ι δ ζ η θ ι ρ σ μ ν E α β γ δ site web E α β γ δ = − 24 E α β γ δ E ρ β γ δ = − six δ ρ α E α β γ δ E ρ σ γ δ = − 2 δ ρ σ α β E α β γ δ E ρ σ θ δ = − δ ρ σ θ α β γ . displaystyle commence aligned E_ alpha beta gamma delta E_ rho sigma mu nu &=-g_ alpha zeta g_ beta eta g_ gamma theta g_ delta iota delta _ rho sigma mu nu ^ zeta eta theta iota E^ alpha beta gamma delta E^ rho sigma mu nu &=-g^ alpha zeta g^ beta eta g^ gamma theta g^ delta iota delta _ zeta eta theta iota ^ rho sigma mu nu E^ alpha beta gamma delta E_ alpha beta gamma delta &=-24E^ alpha beta gamma delta E_ rho beta gamma delta &=-sixdelta _ rho ^ alpha E^ alpha beta gamma delta E_ rho sigma gamma delta &=-2delta _ rho sigma ^ alpha beta E^ alpha beta gamma delta E_ rho sigma theta delta &=-delta _ rho sigma theta ^ alpha beta gamma ,.end aligned

where gab may be the representation in the metric in that coordinate process. We can easily in the same way think about a contravariant Levi-Civita tensor by raising the indices Using the metric as normal,

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