maxCol -- Returns a submatrix form by a maximal set of linear independent columns.

Synopsis

• Usage:

  MM = maxCol(m)

• Inputs:
  • m, a matrix
• Optional inputs:
  • Strategy => ..., default value null, choose between Exact and Numeric algorithms
• Outputs:
  • M, a matrix
  • c, a list

Description

From a given m x n - Matrix of rank r, maxCol returns a submatrix M form by a maximal set of linear independent columns, and the list of columns c chosen.

i1 : M = matrix {{1,2,3},{1,2,3},{4,5,6},{4,5,6}}

o1 = | 1 2 3 |
     | 1 2 3 |
     | 4 5 6 |
     | 4 5 6 |

              4        3
o1 : Matrix ZZ  <--- ZZ

i2 : maxCol M;

NOTE: because of the necessity of rank the base field need to be QQ for doing generic evaluation. If not, one gets the message: expected an affine ring (consider Generic=>true to work over QQ).

i3 : R=QQ[a..g]

o3 = R

o3 : PolynomialRing

i4 : M = matrix {{a,a,b},{c,c,d},{e,e,f},{g,g,g}}

o4 = | a a b |
     | c c d |
     | e e f |
     | g g g |

             4       3
o4 : Matrix R  <--- R

i5 : maxCol M

o5 = {| a b |, {0, 2}}
      | c d |
      | e f |
      | g g |

o5 : List

See also

• maxMinor -- Returns a maximal minor of the matrix of full rank.
• rank -- compute the rank