it's an unfortunate terminology collision. - array languages: rank is the dimensionality of an array, i.e. a vector is rank-1, a matrix is rank-2, a N-D array

it's an unfortunate terminology collision. - array languages: rank is the dimensionality of an array, i.e. a vector is rank-1, a matrix is rank-2, a N-D array is rank-N - linear algebra: rank is the number of linearly-independent columns (and also rows) So for example, if you have a 5x5 matrix where 4 of the columns are linearly independent, it would be rank-4 in the linear algebra sense, and rank-2 in the array language sense. I guess (though I've never really thought of it before) that you could say that the array-language definition is the rank (in the linear algebra sense) of the index space. Not sure if that's intentional.