rank; number of dimensions
Technical term in computing and mathematics for the rank or dimensionality of an array, matrix, or data structure.
The rank of this array is 3.
Please check the number of dimensions of the matrix.
ランク is a more general term for rank, used in many contexts, while 次元数 is a technical term limited to computing and mathematics.
dimensionless number
Compound of 次元 (dimension) + 数 (number). The exact historical derivation is uncertain, but the term is a straightforward technical coinage.