Cofactors
Cofactors: The cofactor $C_{ij}$ of entry $a_{ij}$ is $C_{ij} = (-1)^{i+j} M_{ij}$, where $M_{ij}$ is the minor (determinant of the submatrix obtained by deleting row $i$ and column $j$). The determinant can be computed by cofactor expansion along any row or column: $\det(A) = \sum_j a_{ij}C_{ij}$.
Parents
Children
- Definition of cofactor/submatrix of a matrix
- Definition of determinant of a matrix as a cofactor expansion across the first row
- The determinant of a matrix can be computed as a cofactor expansion across any row.
- The determinant of a matrix can be computed as a cofactor expansion down any column.
- The inverse of a matrix can be expressed in terms of its matrix of cofactors.
- Cramer's rule