Ndims

Ndims, short for the number of dimensions, is a term used to describe the number of axes in an array, tensor, or geometric object. It indicates how many directions along which the data is organized. In mathematics and computer science, ndims helps distinguish simple data like scalars from more complex, multi-dimensional data.

In common usage, a scalar has ndims 0, a vector has ndims 1, a matrix has ndims 2, and higher-order tensors have ndims equal to the number of axes. For example, a 3x4 matrix has ndims 2, while a 3x3x3 tensor has ndims 3. The concept is important for understanding operations such as indexing, broadcasting, and linear algebra, where the alignment of dimensions matters.

Ndims is distinct from related terms. Shape describes the lengths along each axis, size is the total number of elements, and rank can refer to different ideas in different contexts (such as linear independence or tensor decomposition). Broadcasting and arithmetic on arrays often rely on both ndims and shape to determine compatibility.

Language- and library-specific usage varies. In Python's NumPy, the property array.ndim reports ndims; MATLAB provides the ndims function; Julia offers ndims(x) to query the number of dimensions; R uses the dim attribute or length(dim(x)) for the same purpose. These tools use ndims to guide indexing, reshaping, and operations that require compatible dimensionality.

Understanding ndims helps ensure correct data manipulation, efficient computation, and correct interpretation of multi-dimensional data across disciplines.