anonanon 152k1212 gold badges233233 silver badges398398 bronze badges $endgroup$ 4 $begingroup$ That is perfect many thanks a bunch! I also posted a similar issue in this article: math.stackexchange.com/concerns/2135276/… that you might have some insight on? $endgroup$
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or Minkowski House. The values on the Levi-Civita image are impartial of any metric tensor and coordinate technique. Also, the specific term "image" emphasizes that it is not a tensor due to the way it transforms involving coordinate techniques; nonetheless it can be interpreted for a tensor density.
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Gamers may also elect to add further bets, for instance 3D or second bets, which supply lessen payouts but greater possibilities of profitable.
Sure, there are still a lot of open questions and regions of analysis relevant to Levi-Civita properties in four Proportions.
Firstly english just isn't my mom tongue sorry. I need to talk to If you're able to enable me with a number of the properties on the levi-civita image.
The Levi-Civita image allows the determinant of the sq. matrix, and also the cross merchandise of two vectors in 3-dimensional Euclidean House, for being expressed in Einstein index notation.
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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 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 &=-twodelta _ rho sigma ^ alpha beta E^ alpha beta gamma delta E_ rho sigma theta delta &=-delta _ rho sigma theta ^ alpha beta gamma ,.end aligned
E α β γ δ = g α ζ levis4d 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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