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

## Synopsis

• Usage:
MM = maxMinor(Mat)
• 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, 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 .