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

## Synopsis

• Usage:
MM = maxCol(m)
• Inputs:
• m,
• Optional inputs:
• Strategy => ..., default value null, choose between Exact and Numeric algorithms
• Outputs:

## 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

## Ways to use maxCol :

• "maxCol(Matrix)"

## For the programmer

The object maxCol is .