@BrianM.Scott 's answer to this question Q: 3-dimensional array suggests that there is no standard concept of symmetry for 3-, 4-, N-dimensional arrays, in constrast to the case for 2-D arrays, as in linear algebra for matrices. Are there alternative definitions of symmetry for higher-dimensional arrays? Are there specific definitions that are widely used in certain contexts, e.g. in tensor calculus?
(I don't have a specific need; I'm trying to help implement a symmetry test for a matrix library [core.matrix for the Clojure language]. Since the library allows higher-dimensional arrays, there's a question about whether there is a natural choice for what the symmetry test should return for higher-dimensional arrays.)