ijk

ijk is a conventional trio of letters used in many technical fields to represent indices, coordinates, or directions in three-dimensional contexts.

In mathematics, i, j, and k are standard indices in multi-index notation. When Einstein summation is employed, repeated indices imply summation across their range, typically from 1 to 3 in 3D problems or 1 to n in higher dimensions.

In physics and geometry, i, j, k are also used for the standard Cartesian basis vectors i-hat, j-hat, and k-hat, which point along the x-, y-, and z-axes, respectively.

In computing and data analysis, ijk often denotes a triple index for accessing elements of a three-dimensional array or grid, such as data[i][j][k], with i, j, k representing positions along the three axes.

The triple index can appear in the Levi-Civita symbol ε_ijk, which is antisymmetric in its indices and plays a central role in representing cross products, determinants, and oriented volumes in three dimensions.

In practice, the exact meaning of ijk depends on context, but the convention is widespread due to its intuitive alignment with three axes or dimensions.