aij2ij
aij2ij is a compact, informal notation sometimes used in mathematical or computational literature to denote a transformation that takes a two-index object aij (such as a matrix A with entries aij) and maps it to another two-index object with indices that may be relabeled or permuted. It is not a universally standardized operator, but a shorthand for describing a class of index-mapping operations.
Formally, let A be a matrix or rank-2 tensor with entries aij, where i and j range
Examples illustrate the idea. Transposition is the familiar case where aij2ij yields a matrix B with Bij
Usage and note. In texts that employ aij2ij, the exact meaning depends on the author’s convention, so