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A minor is the reduced determinant of a determinant expansion that is formed by omitting the th row and th column of a matrix . So, for example, the minor of the above matrix is given by

The th minor can be computed in the Wolfram Language using

  Minor[m_List?MatrixQ, {i_Integer, j_Integer}] :=
    Det[Drop[Transpose[Drop[Transpose[m], {j}]],
      {i}]]

The Wolfram Language's built-in Minors[m] command instead gives the minors of a matrix obtained by deleting the st row and st column of , while Minors[m, k] gives the th minors of . The Minor code above therefore corresponds to th entry of

  MinorMatrix[m_List?MatrixQ] := Map[Reverse,
    Minors[m], {0, 1}]

i.e., the definition Minors[m, {i, j}] is equivalent to MinorMatrix[m][[i, j]].

See also

Cofactor, Determinant, Determinant Expansion by Minors, Submatrix

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References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 169-170, 1985. Lichtblau, D. "Symbolic FAQ." https://library.wolfram.com/infocenter/Conferences/325/.Muir, T. "Minors and Expansion." Ch. 4 in A Treatise on the Theory of Determinants. New York: Dover, pp. 53-137, 1960.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, p. 235, 1990.

Referenced on Wolfram|Alpha

Minor

Cite this as:

Weisstein, Eric W. "Minor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Minor.html

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