cofactor expansion | Laplacian determinant expansion by minors | Laplacian expansion

Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for small matrices, techniques such as Gaussian elimination are much more efficient when the matrix size becomes large. Let left bracketing bar A right bracketing bar denote the determinant of an n×n matrix A, then for any value i = 1, ..., n, left bracketing bar A right bracketing bar = sum_(j = 1)^n (-1)^(i + j) a_(i j) M_(i j), where M_(i j) is a so-called minor of A, obtained by taking the determinant of A with row i and column j "crossed out."

cofactor | condensation | determinant | Gaussian elimination