compute a basis for the column space of a matrix - Maple Help

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MTM[colspace] - compute a basis for the column space of a matrix

 Calling Sequence colspace(A)

Parameters

 A - matrix, vector, array, or scalar

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $A:=\mathrm{Matrix}\left(\left[\left[1,2,3+I\right],\left[a,2,0.2\right],\left[2a,4,0.4\right]\right]\right)$
 ${A}{:=}\left[\begin{array}{ccc}{1}& {2}& {3}{+}{I}\\ {a}& {2}& {0.2}\\ {2}{}{a}& {4}& {0.4}\end{array}\right]$ (1)
 > $\mathrm{colspace}\left(A\right)$
 $\left[\begin{array}{rr}{1}& {0}\\ {0}& {1}\\ {0}& {2}\end{array}\right]$ (2)