Dual Scalar

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Let , , and be three polar vectors, and define

			(1)
			(2)

where det is the determinant. The is a third-tensor rank tensor, then the dual scalar is defined as

V=1/(3!)epsilon_(ijk)V_(ijk)=|A_1 B_1 C_1; A_2 B_2 C_2; A_3 B_3 C_3|,

(3)

where is the permutation tensor.

See also

Dual Tensor, Permutation Tensor

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References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, p. 133, 1985.

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Cite this as:

Weisstein, Eric W. "Dual Scalar." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DualScalar.html

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