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

- Usage:
    `MM = maxMinor(Mat)`
- Inputs:
  - m, a matrix
- Optional inputs:
  - Strategy => ..., default value null, choose between Exact and Numeric algorithms
- Outputs:
  - a matrix

## Description

From a given m x n - Matrix of rank r, maxMinor returns an r x r full rank Matrix. This method uses twice the method maxCol by transposing twice.

    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 : maxMinor M

    o2 = | 1 2 |
         | 4 5 |

                  2       2
    o2 : Matrix ZZ  <-- ZZ

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 : maxMinor M

    o5 = | a b |
         | c d |

                 2      2
    o5 : Matrix R  <-- R

## See also

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

## Ways to use maxMinor:

- `maxMinor(Matrix)`

## For the programmer

The object maxMinor is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/EliminationMatrices.m2:1149:0.