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Minors

Minors[m]
gives the minors of a matrix m.
Minors[m, k]
gives k^(th) minors.
  • For an nn matrix the (i, j)^(th) element of Minors[m] gives the determinant of the matrix obtained by deleting the (n-i+1)^(th) row and the (n-j+1)^(th) column of m.
  • Map[Reverse, Minors[m], {0, 1}] makes the (i, j)^(th) element correspond to deleting the i^(th) row and j^(th) column of m.
  • Minors[m, k] gives the determinants of the kk submatrices obtained by picking each possible set of k rows and k columns from m.
  • Each element in the result corresponds to taking rows and columns with particular lists of positions. The ordering of the elements is such that reading across or down the final matrix the successive lists of positions appear in lexicographic order.
  • For an n1n2 matrix Minors[m, k] gives a matrix.
  • Minors[m, k, f] applies the function f rather than Det to each of the submatrices picked out.
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