Determinant Expansion by Minors

Also known as Laplacian Determinant Expansion by Minors. Let $\vert{\hbox{\sf M}}\vert$ denote the Determinant of a Matrix M, then

$$\vert{\hbox{\sf M}}\vert = \sum_{i=1}^k (-1)^{i+j}a_iM_{ij},$$

where $M_{ij}$ is called a Minor,

$$\vert{\hbox{\sf M}}\vert = \sum_{i=1}^k a_iC_{ij},$$

where $C_{ij}$ is called a Cofactor.

See also Cofactor, Determinant

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 169-170, 1985.