- 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.
Rank in the array language terminology seems to be synonymous with tensor order (sometimes called tensor rank). Ken Iverson (APL's creator) was a mathematician, so I'm not that surprised to learn the term came from a branch of math.
- 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.