Tensors

Axiality and rhombicity

In physics and mathematics, axiality and rhombicity are two characteristics of a symmetric second-rank tensor in three-dimensional Euclidean space, describing its directional asymmetry. Let A denote a second-rank tensor in R3, which can be represented by a 3-by-3 matrix. We assume that A is symmetric. This implies that A has three real eigenvalues, which we denote by , and . We assume that they are ordered such that The axiality of A is defined by The rhombicity is the difference between the smallest and the second-smallest eigenvalue: Other definitions of axiality and rhombicity differ from the ones given above by constant factors which depend on the context. For example, when using them as parameters in the irreducible spherical tensor expansion, it is most convenient to divide the above definition of axiality by and that of rhombicity by . (Wikipedia).

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Related pages

Mathematics | Symmetric tensor | Spin (physics) | Matrix (mathematics) | Euclidean space | Tensor