antisymmetric tensor

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antisymmetric tensor

[¦an·tē·si¦me·trik ′ten·sər]
(mathematics)
A tensor in which interchanging two indices of an element changes the sign of the element.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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If we define a second-rank anti-symmetric tensor B by
Taking a local coordinate basis [[theta].sup.i] = [dx.sup.i], a Pfaffian p-form [omega] is the completely anti-symmetric tensor field
where the tensor [u.sup.[mu];v] is a combination of symmetric and anti-symmetric tensors. Lowering index v and contracting, we get the volume dilatation of the spacetime continuum

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