ColumnSpace - Maple Help

Student[LinearAlgebra]

 RowSpace
 return a basis for the row space of a Matrix
 ColumnSpace
 return a basis for the column space of a Matrix

 Calling Sequence RowSpace(A, options) ColumnSpace(A, options)

Parameters

 A - Matrix options - (optional) parameters; for a complete list, see LinearAlgebra[RowSpace]

Description

 • The RowSpace(A) (ColumnSpace(A)) command returns a list of row (column) Vectors that form a basis for the Vector space spanned by the rows (columns) of Matrix A.  The Vectors are returned in canonical form with leading entries 1.
 • The row space (column space) of a zero Matrix is the empty list.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right):$
 > $A≔⟨⟨1,2,0⟩|⟨0,2,6⟩|⟨0,1,3⟩|⟨1,1,-3⟩⟩$
 ${A}{≔}\left[\begin{array}{cccc}{1}& {0}& {0}& {1}\\ {2}& {2}& {1}& {1}\\ {0}& {6}& {3}& {-3}\end{array}\right]$ (1)
 > $\mathrm{RowSpace}\left(A\right)$
 $\left[\left[\begin{array}{cccc}{1}& {0}& {0}& {1}\end{array}\right]{,}\left[\begin{array}{cccc}{0}& {1}& \frac{{1}}{{2}}& {-}\frac{{1}}{{2}}\end{array}\right]\right]$ (2)
 > $\mathrm{ColumnSpace}\left(A\right)$
 $\left[\left[\begin{array}{c}{1}\\ {0}\\ {-6}\end{array}\right]{,}\left[\begin{array}{c}{0}\\ {1}\\ {3}\end{array}\right]\right]$ (3)