antisymmetric dyadic

antisymmetric dyadic

[¦an·tē·si¦me·trik dī′ad·ik]
(mathematics)
A dyadic equal to the negative of its conjugate.
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(vi) Finally, let us assume that [??] is an antisymmetric dyadic, which can be expressed in terms of some bivector A in the form
Since the last expression is an antisymmetric dyadic and [mathematical expression not reproducible] is a symmetric dyadic or zero, we have
and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is an antisymmetric dyadic. The bivector D is simple because it satisfies
Since a simple bivector can be expressed in terms of two vectors as D = [d.sub.1] [conjunction] [d.sub.2], the antisymmetric dyadic satisfies
In the converse case, it either corresponds to a P-solution or a special Q-solution with antisymmetric dyadic [??].
* For [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] we have a Q-solution with antisymmetric dyadic [??].
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