[[Linear algebra MOC]]
# Minor

Let $T \in \opn M_{n,n}(R)$ be a [[Matrix algebra over a ring|square matrix]].
The **$(i,j)$ minor** $M_{i,j}$ is the [[Matrix determinant|determinant]] of the submatrix of $T$ with the $i$th row and $j$th column deleted.
The corresponding **cofactor** is $C_{ij} = (-1)^{i+j}M_{i,j}$,
with the **cofactor matrix** defined as
$$
\begin{align*}
\opn{cof} T = (C_{ij})
\end{align*}
$$

## See also

- [[Adjugate matrix]]

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