# conjugate directions

## conjugate directions

[′kän·jə·gət di′rek·shənz]
(mathematics)
For a point on a surface, a pair of directions, one of which is the direction of a curve on the surface through the point, while the other is the direction of the characteristic of the planes tangent to the surface at points on the curve.
References in periodicals archive ?
Therefore, directions of fields [??], [??] and [??] are a triad of conjugate directions with respect to tensor [mathematical expression not reproducible] and constitutes a local basis, whose reciprocal one is formed by directions of [??], [??] fields and [nabla]S.
For instance, the orthogonality of vectors [[bar.e].sup.1] and [[bar.e].sub.3] (and from Cauchy's theorem [18], [[bar.e].sup.3] and [[bar.e].sub.1]) implies that [[bar.e].sup.1] and [[bar.e].sup.3] are conjugate directions. In order to visualize these concepts, a section of Cauchy's quadric of revolution is shown (see Fig.
It must be noted that principal directions of a tensor are also conjugate directions. Conjugation arises as a broader concept than that of principal directions (a particular case, where [[bar.[GAMMA]].sub.v] is collinear with V), but keeping the algebraic property of diagonalisation of tensors, if expressed in covariant components.
We have shown that directions of fields [bar.D], [bar.B] and [bar.[upsilon]] (ray velocity) are a triad of conjugate directions with respect to the inverse relative dielectric permittivity tensor and constitutes a local basis, whose reciprocal one is formed by directions of [bar.E], [bar.H] fields and wavevector [bar.k].

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