linguistic:paraphrasing, structural:reformatting
Column rank – dimension of column space

The rank of A is the maximal number of linearly independent columns c 1, c 2, …, c k {\displaystyle \mathbf {c} _{1},\mathbf {c} _{2},\dots,\mathbf {c} _{k}} of A; this is the dimension of the column space of A (the column space being the subspace of F generated by the columns of A, which is in fact just the image of the linear map f associated to A).