The Minor(A, r, c) function, where A is an m x m (square) Matrix, returns the determinant of the (m-1) x (m-1) submatrix found by deleting the rth row and the cth column of A.  This is equivalent to Minor(A, r, c, 'output'='determinant').

The Minor(A, r, c, 'output'='matrix') function, where A is an m x n Matrix, returns the (m-1) x (m-1) submatrix found by deleting the rth row and the cth column of A.

If the out parameter includes 'matrix', then the constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).

If the determinant of the submatrix is to be returned, the meth option can be used to select the method by which that determinant is computed.  See Determinant for the possible methods.

This function is part of the LinearAlgebra package, and so it can be used in the form Minor(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[Minor](..).

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\:$

$A≔⟨⟨a\left|b\right|c⟩\,⟨d\left|e\right|f⟩\,⟨g\left|h\right|i⟩⟩$

$A≔\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]$

$\mathrm{Minor}\left(A\,3\,3\right)$

$ae-bd$

$\mathrm{Minor}\left(A\,1\,2\,\mathrm{output}=\left['\mathrm{matrix}'\,'\mathrm{determinant}'\right]\,\mathrm{method}='\mathrm{minor}'\right)$

$\left[\begin{array}{cc}d& f\\ g& i\end{array}\right],di-fg$

$B≔⟨⟨1\,2\,3⟩\left|⟨4\,5\,6⟩\right|⟨7\,8\,9⟩|⟨0\,1\,2⟩⟩$

$B≔\left[\begin{array}{cccc}1& 4& 7& 0\\ 2& 5& 8& 1\\ 3& 6& 9& 2\end{array}\right]$

$\mathrm{Minor}\left(B\,2\,2\,\mathrm{output}='\mathrm{matrix}'\,\mathrm{datatype}=\mathrm{float}\right)$

$\left[\begin{array}{ccc}1.& 7.& 0.\\ 3.& 9.& 2.\end{array}\right]$