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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


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

© 1996-9 Eric W. Weisstein