6.47.14  Subspace generated by the columns of a matrix: colspace

The colspace command finds a basis for the column space of a matrix.

• colspace takes one mandatory argument and one optional argument:
  • A, a matrix.
  • Optionally, var, a variable name.
• colspace(A ⟨var⟩) returns a matrix whose columns are a basis of the subspace generated by the columns of A. With the optional argument var, Xcas will store the dimension of the subspace generated by the columns of A.

Examples.

• Input:
  colspace([[1,1,2],[2,1,3],[3,1,4]])
  Output:

  ⎡ ⎢ ⎢ ⎣

  −1 0 0 −1 1 −2

  ⎤ ⎥ ⎥ ⎦

• Input:
  colspace([[1,1,2],[2,1,3],[3,1,4]],dimension)
  Output:

  ⎡ ⎢ ⎢ ⎣

  −1 0 0 −1 1 −2

  ⎤ ⎥ ⎥ ⎦

  then input:
  dimension
  Output:

  2