Observe that the coordinates of the vector (with respect to the basis ) appear in the jth column of . The vectors are therefore sometimes called the column vectors of . With this terminology, the range of is spanned by the column vectors of . This is useful because it allows concrete calculations. Matrices yield examples of linear maps: if is a real matrix, then describes a linear map (see Euclidean space).
Observe that the coordinates of the vector (with respect to the basis ) appear in the jth column of . The vectors are therefore sometimes called the column vectors of . With this terminology, the range of is spanned by the column vectors of . This is useful because it allows concrete calculations. Matrices yield examples of linear maps: if is a real matrix, then describes a linear map (see Euclidean space).