The Levi-Civita symbol allows the determinant of the square matrix, along with the cross item of two vectors in 3-dimensional Euclidean Room, to become expressed in Einstein index notation.
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The importance of Levi-Civita Houses in 4 Proportions lies in their function during the mathematical description of 4-dimensional Areas, that have crucial purposes in physics and cosmology. They even have programs in other fields such as Laptop or computer graphics and robotics.
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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ε i j ε i n = δ j n displaystyle varepsilon _ ij varepsilon ^ in = delta _ j ^ n