Minor (linear algebra)

In linear algebra, a minor of a matrixA is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns. Minors obtained by removing just one row and one column from square matrices (first minors) are useful for calculating matrix cofactors, which are useful for computing both the determinant and inverse of square matrices. The requirement that the square matrix be smaller than the original matrix is often omitted in the definition.

The cofactors ${\displaystyle C_{ij}}$ are also the partial derivatives with respect to the matrix entries of the determinant map ${\displaystyle {\text{det}}:{\text{Mat}}(n,\mathbb {R} )\to \mathbb {R} }$ which takes a matrix ${\displaystyle (a_{i,j})_{i,j\in \{1,\dots ,n\}}}$ to its determinant:

${\displaystyle {\frac {{\text{d}}({\text{det}})}{{\text{d}}a_{ij}}}=C_{ij}}$