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