Minors

Minors[m]

gives the minors of a matrix m.

Minors[m,k]

gives the k ^(th) minors.

Details

  • For an × matrix the ^(th) element of Minors[m] gives the determinant of the matrix obtained by deleting the ^(th) row and the ^(th) column of m.
  • Map[Reverse,Minors[m],{0,1}] makes the ^(th) element correspond to deleting the ^(th) row and ^(th) column of m.
  • Minors[m] is equivalent to Minors[m,n-1].
  • Minors[m,k] gives the determinants of the k×k 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 × matrix Minors[m,k] gives an × matrix.
  • Minors[m,k,f] applies the function f rather than Det to each of the submatrices picked out.

Examples

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Basic Examples  (2)

Minors of a 3×3 matrix:

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Out[1]//MatrixForm=
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Out[2]//MatrixForm=

2×2 minors of a 2×3 matrix:

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Out[1]//MatrixForm=
In[2]:=
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Scope  (2)

Applications  (3)

Properties & Relations  (5)

Neat Examples  (1)

See Also

Det  Delete  Tr  Band

Tutorials

Introduced in 1988
(1.0)
| Updated in 1999
(4.0)