The column spacecolsp𝐴 of a matrix 𝐴 is the span of its columns, linalg
or considered as a Linear map,
the target Vector subspace.
Hence it is sometimes referred to as the range or the image of a matrix.
Dually, the row spacerowsp𝐴 of a matrix 𝐴 is the span of its rows. linalg
It is therefore the range of linear functionals made by premultiplying the matrix by a linear functional.
Basis
A basis for a row space can be performed by performing Gaußian elimination on the matrix 𝐴,
since all non-zero rows of a matrix in Row echelon form are independent.
Likewise, the basis of a column space of a matrix 𝐴
is found by performing gaussian elimination on the transpose 𝐴𝖳,
and then transposing the results back to column vectors.