The colspace(A) function returns a matrix R, where the columns of R are vectors that form a basis for the vector space spanned by the columns of the matrix A. The vectors are returned in canonical form with leading entries of 1.

When A is the zero matrix, colspace(A) returns the empty matrix.

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,3+\mathrm{I}\right]\,\left[a\,2\,0.2\right]\,\left[2a\,4\,0.4\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3+\mathrm{I}\\ a& 2& 0.2\\ 2a& 4& 0.4\end{array}\right]$

$\mathrm{colspace}\left(A\right)$

$\left[\begin{array}{cc}1& 0\\ 0& 1\\ 0& 2\end{array}\right]$