In
linear algebra, the
minor of a
matrix is the
determinant of the matrix obtained after deleting a row <math>i</math> and column <math>j</math>, and is written <math>M_{ij}</math>.
For example, given the matrix
- <math>\begin{pmatrix}
1 & 4 & 7 \\
3 & 0 & 5 \\
-1 & 9 & 11 \\
\end{pmatrix}</math>
and suppose we wish to find the minor of the (2,3) entry. We consider the matrix with row 2 and column 3 removed (note the following is not standard notation!):
- <math>\begin{pmatrix}
1 & 4 & ! \\
! & ! & ! \\
-1 & 9 & ! \\
\end{pmatrix}</math>
This gives:
- <math>M_{23}=\begin{vmatrix}
1 & 4 \\
-1 & 9 \\
\end{vmatrix}=9+4=13</math>
Specially signed minors, known as cofactors, are useful in calculating the inverse of small matrices.