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= δ i l ( δ j m δ k n − δ j n δ k m ) − δ i m ( δ j l δ k n − δ j n δ k l ) + δ i n ( δ j l δ k m − δ j m δ k l ) .

or Minkowski Place. The values in the Levi-Civita image are impartial of any metric tensor and coordinate technique. Also, the specific term "image" emphasizes that it's not a tensor as a consequence of how it transforms among coordinate methods; however it might be interpreted being a tensor density.

These properties are important for comprehending the habits with the tensor in several coordinate methods.

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The Levi-Civita tensor is Employed in the Einstein discipline equations to express the curvature of spacetime in terms of the Electrical power and momentum of subject and radiation.

The Levi-Civita symbol makes it possible for the determinant of a square matrix, as well as cross solution of two vectors in a few-dimensional Euclidean Room, to become expressed in Einstein index notation.

Using the capital pi notation Π for ordinary multiplication of quantities, an express expression with the image is:[citation essential]

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The covariant Levi-Civita tensor (often known as the Riemannian quantity form) in any coordinate system that matches the selected orientation is

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