Dual Scalar

Let A, B, and C be three polar vectors, and define

V_(ijk)=|A_i B_i C_i; A_j B_j C_j; A_k B_k C_k|
=det[A B C],

where det is the determinant. The V_(ijk) 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|,

where epsilon_(ijk) is the permutation tensor.

See also

Dual Tensor, Permutation Tensor

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

Referenced on Wolfram|Alpha

Dual Scalar

Cite this as:

Weisstein, Eric W. "Dual Scalar." From MathWorld--A Wolfram Web Resource.

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